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【新课标】2012届高三数学二轮精品专题卷10 解析几何(直线与圆、椭圆、双曲线和抛物线)

letters and calls, a nd do pra ctical t hings for t he masse s com bine g ood, effective through rea chi ng pe ople at the servi ce of the "last mile". T hird, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Ji npi ng stresse d devel opme nt of innova tion forest restructuring, revitalization of the ol d industrial bases i n Northeast Chi na is the State's maj or strategy, Central ha s iss ued compr ehe nsive opi nions of revitalizi ng Nort heast China and other old i ndustrial ba ses, t he CPC Ce ntral Committee on revitalizati on in Nort heast China w ere ... V igorous determination does not waver, the w ork does not sl acken off. Be firm with in the devel opment has more t o do with har d, and not muddle al ong, passiv e ina ction. To re ly on t heir ow n efforts, ca n't wait , ca n't wait, stand still. T his not only pr ovides new opportunities for development in our regi on, a nd gave us ne w requirements. We must s eize the opportunity, full use of national policy, ha s to be m ore com plicate d, to start and target, give full play to t he initiative of leadi ng ca dres at all level s, active, active, focusi ng on building new moment um for devel opment , accelerating transformation of forest devel opment . To im plement t he ne w devel opme nt philos ophy. Phi los ophy is the action gui de, new ideas a nd new deve lopme nts. Carrying out innov ation, coor dinati on a nd development of green, ope n, s hared i deas, must be mea surabl e, dire ct acti on wit h ne w devel opme nt concepts, trai ning ca dres. In a new development concept a s a yardsti ck. Esta blished i n line w ith t he new conce pt of evaluati on system a nd eval uation criteri on, embodies the new devel opment poli cy, organizati on, ma ndate im plementat ion, always mea sure d by the new devel opment phil os ophy, conti nuous correction of forest transition course. In a new development concept for t he pat h comma nd. A s part of the implementati on of the ne w devel opme nt philosophy followe d and acti on gui deli nes, f irmly adj usted, corre cted a nd rej ect uns uitable , ina ppropriate a nd eve n agains t the new devel opment i deas, be haviors a nd practi ces, more pragmatic approa ch base d on a br oad visi on, and creatively carry out e col ogica l construction, industrial devel opme nt, im provi ng pe opl e's liveli hood, such as t he w ork to ensure t hat new devel opment i deas take root in forest area s. I n a new dev elo pment concept for wea pon traini ng ca dre. Educati on lea ders "in t he ne w, nothi ng" two articl es, e nha nci ng vitality and power. Combi ned devel opme nt "six big industry", a nd impl ementation "three big engineering", a nd create "two big e nvironment", strengt heni ng on new devel opme nt, and new e conomy concept of learni ng, and grasp and usi ng, real put thoug ht and action unified to new development conce pt up, at with new development concept arme d himse lf, and gui de pra ctice , effective do a dvocate innovation, a nd focuse d on coor dinati on, a nd a dvocate gre en, a nd t hick plant open, and adva nce share d. Second, we must rely on Scie nce a nd te chnol ogy affects. Te chnical innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

绝密★启用前

2012 届高三数学二轮精品专题卷:专题 10 解析几何(直线 与圆、椭圆、双曲线和抛物线)
考试范围:解析几何(直线与圆、椭圆、双曲线和抛物线) 一、选择题(本大题共 10 小题;每小题 5 分,共 50 分.在每小题给出的四个选项中,只有一项是符合题 目要求的) 1 ( . ) A. ? 直 线

xt

?
7

?y a?0

n











? 7


B.

? 7

C.

5? 7

D.

6? 7

2.直线 l1 : x ? y ? 1 ? 0 关于直线 l : x ? 2 对称的直线 l 2 方程为 ( A. 2 x ? y ? 1 ? 0 B. 2 x ? y ? 7 ? 0 C. 2 x ? y ? 4 ? 0 D. x ? y ? 5 ? 0

3 .“ a ? ?2 ” 是 直 线 l1 : ?a ? 1?x ? y ? 2 ? 0 与 直 线 l 2 : ax ? ?2a ? 2? y ? 1 ? 0 互 相 垂 直 的 ( ) A.充分不必要条件 4 ( . ) A.相交 B.相切 C.相离 D.相交或相切 直 线 B.必要不充分条件 C.充要条件 圆 D.既不充分也不必要条件 的 位 置 关 系 为

ax ? by ? a ? b ? 0



x2 ? y2 ? 2

5.已知点 P 在圆 x 2 ? y 2 ? 4 x ? 4 y ? 7 ? 0 上,点 Q 在直线上 y ? kx 上,若 PQ 的最小值为 2 2 ? 1 , 则k = ( A.1 6 . 若 椭 圆 ( ) A. ? , ? ) B. ?1 C.0 D.2

? 3 2? ? , 则 m 的 取 值 范 围 是 , x 2 ? my2 ? 1 的 离 心 率 e ? ? ? 3 2 ? ? ?
?1 2? , ? ? ?1,2 ? ?2 3?

?1 2? ?2 3?

B. ?1, 2 ?

C. ?

D. ?

?1 ? ,2 ? ?2 ?

7.已知中心在原点,焦点在坐标轴上的双曲线的一条渐近线方程为 3x ? y ? 0 ,则该双曲线的离心率为 ( A. )

2 3 3

B. 3

C.2 或

2 3 3

D.

2 3 或 3 3

8.M 是抛物线 y 2 ? 4 x 上一点,且在 x 轴上方,F 是抛物线的焦点,以 x 轴的正半轴为始边,FM 为终边 构 ( A.2 成 ) B.3 C.4 D.6 的 最 小 的 角 为 60 ° , 则

FM ?

livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as th e starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relief a nd development work . Impl ementing poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stations, Tahe, Pine Ri dge research, visite d ma ny of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack. Poverty alleviati on a nd development li es in pre ci se, a ccurate. Pre sent, i n order to find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepre ne urs hip for poverty eradication poverty eradi cation, educati on, poverty all eviation, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by the State Council on furt her pr omoting urba nization c onstructi on of new opi nions, propos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese characteristi cs. A ccor ding t o distri ct-wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dential a nd farm tour towns a nd v illages, f orming one village one product, a feature pattern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted support to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of

letters and calls, a nd do pra ctical t hings for t he masse s com bine g ood, effective through rea chi ng pe ople at the servi ce of the "last mile". T hird, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Ji npi ng stresse d devel opme nt of innovation forest restru cturing, revitalization of the ol d industrial bases i n Northeast Chi na is the State's maj or strategy, Central ha s iss ued compr ehe nsive opi nions of revitalizi ng Nort heast China and other old i ndustrial ba ses, t he CPC Ce ntral Committee on revitalizati on in Nort heast China w ere ... V igorous determination does not waver, the w ork does not sl acken off. Be firm with in the devel opment has more t o do with har d, and not muddle al ong, passiv e ina ction. To re ly on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only pr ovides new opportunities for development in our regi on, a nd gave us ne w requirements. We must s eize the opportunity, full use of national policy, ha s to be m ore com plicate d, to start and target, give full play to t he initiative of leadi ng ca dres at all level s, active, active, focusi ng on building new moment um for devel opment , accelerating t ransformation of forest devel opment . To im plement t he ne w devel opme nt philos ophy. Phi los ophy is the action gui de, new ideas a nd new deve lopme nts. Carry ing out innov ation, coor dinati on a nd development of green, ope n, s hared i deas, must be mea surabl e, dire ct acti on wit h ne w devel opme nt concepts, trai ning ca dres. In a new development concept a s a yardsti ck. Esta blished i n line w ith the new conce pt of evaluati on system a nd eval uation criteri on, embodies the new devel opment poli cy, organizati on, ma ndate im plementation, always mea sure d by the new devel opment phil os ophy, conti nuous correction of forest transition course. In a new development concept for t he pat h comma nd. A s part of the implementati on of the ne w devel opme nt philosophy followe d and acti on gui deli nes, firmly adj usted, cor re cted a nd rej ect uns uitable , ina ppropriate a nd eve n agains t the new devel opment i deas, be haviors a nd practi ces, more pragmatic approa ch base d on a br oad visi on, and creatively carry out e col ogica l construction, industrial devel opme nt, improvi ng pe opl e's liveli hood, such as t he w ork to ensure t hat new devel opment i deas take root in forest area s. I n a new dev elopment concept for wea po n traini ng ca dre. Educati on lea ders "in t he ne w, nothi ng" two articl es, e nha nci ng vitality and power. Combi ned devel opme nt "six big industry", a nd impl ementation "three big engineering", a nd create "two big e nvironment", strengt heni ng on new devel opme nt, and new e conomy concept of learni ng, and grasp and usi ng, real put thoug ht and action unified to new development conce pt up, at with new development concept arme d himse lf, and gui de pra ctice , effective do a dvocate innovation, a nd focuse d on coor dinati on, a nd a dvocate gre en, a nd t hick plant open, and adva nce share d. Second, we must rely on Scie nce a nd te chnol ogy affects. Te chnical innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

9.设抛物线 y 2 ? 8 x 的准线经过中心在原点,焦点在坐标轴上且离心率为 圆 (
2

1 的椭圆的一个顶点,则此椭 2
程 为

的 )



A.

x y2 x2 y2 ? ?1或 ? ?1 12 16 16 12
y2 x2 x2 y2 ? ?1 ? ?1或 16 4 16 12 3

B.

x2 y2 x2 y2 ? ?1或 ? ?1 48 64 64 48
y2 x2 x2 y2 ? ?1 ? ?1或 16 4 4 3 3

C.

D.

10. 已知定点 F1 ?? 2,0 ? 、F2 ?2,0? , 动点 N 满足 ON ? 1 (O 为坐标原点) ,F1M ? 2 NM ,MP ? ? MF2 ?? ? R? ,

F1M ? PN ? 0
( )







P









A.椭圆

B.双曲线

C.抛物线

D.圆

二、填空题(本大题共 5 小题;每小题 5 分,共 25 分.将答案填在题中的横线上) 11.以点 ?? 1,2 ? 为圆心且与直线 y ? x ? 1 相切的圆的标准方程是 .

12.圆 x 2 ? y 2 ? 4 x ? 4 y ? 6 ? 0 上到直线 x ? y ? 5 ? 0 的距离等于

2 的点有 2
2

个.

13.若点 P 在直线 l1 : x ? my ? 3 ? 0 上,过点 P 的直线 l 2 与曲线 C : ?x ? 5? ? y 2 ? 16 只有一个公共点 M, 且 PM 的最小值为 4,则 m ? 14.在平面直角坐标系 xO y 中,椭圆 .
2 2

x

a2

?

y

b2

? 1 ( a > b >0)的离心率为

2 ,以 O 为圆心, a 为半径作 2


圆 M,再过 P?

? a2 ? ,0 ? ? c ? 作圆 M 的两条切线 PA、PB,则 ?APB = ? ?

15.已知以双曲线的两个焦点及虚轴的两个端点为顶点的四边形中,有一个内角的范围是 ? 线的离心率的范围是 .

?? ? ? , ? 则双曲 ?3 2?

三、解答题(本大题共 6 小题;共 75 分.解答应写出文字说明、证明过程或演算步骤) 16. (本题满分 12 分)已知圆 O 的方程为 x 2 ? y 2 ? 16 . (1)求过点 M ?? 4,8 ? 的圆 O 的切线方程; (2)过点 N ?3,0 ? 作直线与圆 O 交于 A、B 两点,求 △OAB 的最大面积以及此时直线 AB 的斜率.

2 17.(本题满分 12 分)将抛物线 x ? ?2 2 y 向上平移 2 个单位长度后,抛物线过椭圆

x2 a2

?

y2 b2

?1( a

> b >0)的上顶点和左右焦点. (1)求椭圆方程;[来源:金太阳新课标资源网 ] (2)若点 P ?m,0 ? 满足如下条件:过点 P 且倾斜角为 F 在以 CD 线段为直径的圆外,试求 m 的取值范围.

5 ? 的直线 l 与椭圆相交于 C、D 两点,使右焦点 6

livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relief a nd development work . Impl em enting poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stations, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack. Poverty alleviati on a nd development li es in pre cise, a ccurate. Pre sent, i n order t o find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepre neurs hip for poverty eradicat ion poverty eradi cation, educati on, poverty all eviation, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by the State Council on furt her pr omoting urba nization constructi on of new opi nions, pro pos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese characteristi cs. A ccor ding t o distri ct -wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dential a nd farm tour towns a nd v illages, f orming one village one product, a feature pattern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted su pport to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of

letters and calls, a nd do pra ctical thi ngs for the ma sses combi ne good, effective thr oug h reaching people at the s ervice of the "last mile". Third, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Jinping stresse d devel opme nt of innovation forest restr uct uring, r evitalizati on of the ol d industrial bases i n Northeast China is the State's maj or strategy, Ce ntral has i ssue d compre hensive opini ons of revitalizing Northea st Chi na and other old i ndustrial bases, t he CPC Ce ntral Committee on revitalization in Nort heast C hina wer e ... V igorous determi nation does not waver, the work does not sla cken off. Be firm with in the development ha s more to do with hard, a nd not muddl e along, pas sive ina ction. To rely on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only provi des new opportunities for devel opme nt in our region, and gave us new requirements . We must s e ize the opportunit y, full use of nati onal poli cy, has to be more compli cated, to start a nd target, give full play to t he initiative of leadi ng cadre s at all levels, a ctive, active, focusing on building ne w moment um for development, a ccel erating t ransformation of forest devel opme nt. To im plement the new development phil os ophy. Phil osophy is t he acti on gui de, new ideas and ne w devel opme nts. Carryi ng out inn ova tion, coor dinati on a nd development of green, open, s hared i deas, m ust be meas urabl e, dire ct action with new development concept s, training cadres . In a new dev elopment concept as a yardstick. E stablis hed i n line with the new conce pt of evaluation system and evaluati on criteri on, embodies t he new deve lopme nt policy, organi zation, mandate im plementati on, always mea sure d by the new dev elopment philosophy, continuous correcti on of forest trans ition course. I n a ne w devel opme nt conce pt for the pat h command. A s part of the impl ementation of the new devel opme nt philosophy followe d and acti on gui deli nes, firmly adjusted, corre cted an d reje ct unsuita ble, ina ppr opriate a nd eve n against the new development i deas, behavi ors and pra ctices , more pragmatic a pproach base d on a broa d visi on, a nd creatively carry out ecologi cal constr uction, i ndustrial devel opme nt, improvi ng pe ople' s livelihood, s uch as the w ork to e nsure t hat new development i deas take root i n forest areas. I n a new development conce pt for weapon traini ng ca dre. Education leaders "in the new, not hing" two arti cles, e nha nci ng vitality and pow er. Combi ned development "six big i ndustry", and im plementation "three big e ngineering", and create "two big envir onment", stre ngthe ning on ne w devel opment , and new economy conce pt of learni ng, and grasp a nd usi ng, real put thought and acti on unified t o new development conce pt up, at wit h new devel opment conce pt armed hims elf, and gui de pra ctice, effective do adv ocate i nnovation, and focused on coor dinati on, a nd a dvocate gree n, a nd thi ck plant ope n, a nd adva nce share d. Second, we must rely on S cience and technology affects. Techni cal innovation is

the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".



18.(本题满分 12 分)已知双曲线,

x2 a2

?

y2 b2

? 1 ( a >0, b >0)左右两焦点为 F1 、 F 2 ,P 是右支上一点,

?1 1 ? PF2 ? F1 F2 , OH ? PF1 于 H, OH ? ? OF 1 ,? ?? , ? . ?9 2?
(1)当 ? ?

1 时,求双曲线的渐近线方程; 3

(2)求双曲线的离心率 e 的取值范围; (3)当 e 取最大值时,过 F1 , F2 , P 的 y 轴的线段长为 8,求该圆的方程.

19.(本题满分 13 分)在平面直角坐标系 xO y 中,过定点 C ? p ,0 ? 作直线 m 与抛物线 y 2 ? 2 px ( p >0)相 交于 A 、 B 两点. (1)设 N ?? p ,0 ? ,求 NA ? NB 的最小值; (2) 是否存在垂直于 x 轴的直线 l , 使得 l 被以 AC 为直径的圆截得的弦长恒为定值?若存在, 求出 l 的 方程;若不存在,请说明理由.

20.(本题满分 13 分)已知椭圆 C 的中心在原点,焦点在 x 轴上,离心率等于 抛物线 x 2 ? 8 3 y 的焦点. (1)求椭圆 C 的方程;

1 2

,它的一个顶点恰好是

(2) P ?2,3? 、 Q?2,?3? 是椭圆上两点,A、B 是椭圆位于直线 PQ 两侧的两动点,①若直线 AB 的斜率 为

1 ,求四边形 APBQ 面积的最大值;②当 A、B 运动时,满足 ?APQ ? ?BPQ ,试问直线 AB 的斜率 2

是否为定值,请说明理由.

livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relief a nd development work . Impl ementing poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stations, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack . Poverty alleviati on a nd development li es in pre cise, a ccurate. Pre sent, i n order to find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepre neurs hip for poverty eradication poverty eradi cation, educati on, poverty all eviation, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by th e State Council on furt her pr omoting urba nization constructi on of new opi nions, propos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese characteristi cs. A ccor ding t o distri ct-wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dential a nd farm tour towns a nd v illages, f orming one village one product, a feat ure pattern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted support to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of

letters and calls, a nd do pra ctical t hings for t he masse s com bine g ood, effective through rea chi ng pe ople at the servi ce of the "last mile". T hird, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Ji npi ng stresse d devel opme nt of innovation forest restru cturing, revitalization of the ol d industrial bases i n Northeast Chi na is the State's maj or strategy, Central ha s iss ued compr ehe nsive opi nions of revitalizi ng Nort heast China and other old i ndustrial ba ses, t he CPC Ce ntral Committee on revitalizati on in Nort heast China w ere ... V igorous determination does not waver, the w ork does not sl acken off. Be firm with in the devel opment has more t o do with har d, and not muddle al ong, passiv e ina ction. To re ly on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only pr ovides new opportunities for development in our regi on, a nd gave us ne w requirements. We must s eize the opportunity, full use of national policy, ha s to be m ore com plicate d, to start and target, give full play to t he initiative of leadi ng ca dres at all level s, active, active, focusi ng on building new moment um for devel opment , accelerating t ransformation of forest devel opment . To im plement t he ne w devel opme nt philos ophy. Phi los ophy is the action gui de, new ideas a nd new deve lopme nts. Carry ing out innov ation, coor dinati on a nd development of green, ope n, s hared i deas, must be mea surabl e, dire ct acti on wit h ne w devel opme nt concepts, trai ning ca dres. In a new development concept a s a yardsti ck. Esta blished i n line w ith the new conce pt of evaluati on system a nd eval uation criteri on, embodies the new devel opment poli cy, organizati on, ma ndate im plementation, always mea sure d by the new devel opment phil os ophy, conti nuous correction of forest transition course. In a new development concept for t he pat h comma nd. A s part of the implementati on of the ne w devel opme nt philosophy followe d and acti on gui deli nes, firmly adj usted, cor re cted a nd rej ect uns uitable , ina ppropriate a nd eve n agains t the new devel opment i deas, be haviors a nd practi ces, more pragmatic approa ch base d on a br oad visi on, and creatively carry out e col ogica l construction, industrial devel opme nt, improvi ng pe opl e's liveli hood, such as t he w ork to ensure t hat new devel opment i deas take root in forest area s. I n a new dev elopment concept for wea po n traini ng ca dre. Educati on lea ders "in t he ne w, nothi ng" two articl es, e nha nci ng vitality and power. Combi ned devel opme nt "six big industry", a nd impl ementation "three big engineering", a nd create "two big e nvironment", strengt heni ng on new devel opme nt, and new e conomy concept of learni ng, and grasp and usi ng, real put thoug ht and action unified to new development conce pt up, at with new development concept arme d himse lf, and gui de pra ctice , effective do a dvocate innovation, a nd focuse d on coor dinati on, a nd a dvocate gre en, a nd t hick plant open, and adva nce share d. Second, we must rely on Scie nce a nd te chnol ogy affects. Te chnical innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

21 .(本题满分 13 分)在平面直角坐 标系中, 已知向 量 a ? ?x, y ? 2? , b ? ?kx, y ? 2??k ? R? ,若

a ?b ? a ?b .
(1)求动点 M ?x, y ? 的轨迹 T 的方程,并说明该方程表示的曲线的形状;

4 时,已知 F1 ?0,?1? 、 F2 ?0,1? ,点 P 是轨迹 T 在第一象限的一点,且满足 PF 1 ? PF2 ? 1 , 3 若点 Q 是轨迹 T 上不同于点 P 的另一点,问是否存在以 PQ 为直径的圆 G 过点 F 2 ,若存在,求出圆 G
(2)当 k ? 的方程,若不存在,请说明理由.[来源:金太阳新课标资源网]

2012 届专题卷数学专题十答案与解析
1. 【命题立意】本题考查直线的一般方程形式、斜率和倾斜角的关系以及正切函数的诱导公式.[来源: 【思路点拨】抓住直线方程 y=kx+b 中斜率为 k,α 为倾斜角,其中 ? ? ?0, ? ? ,当 ? ? 【答案】D【解析】 y ? ? x tan
?
7

]

?
2

时 k ? tan? .

,斜率 k ? ? tan

?
7

?? 6? ? . ? tan ? ? ? ? ? tan 7? 7 ?

2. 【命题立意】本题考查直线的对称和直线方程的求解以及直线上点的确定. 【思路点拨】求出直线 l1 与 x 轴、与 l 的交点坐标,再确定对称点的坐标,最后由两点式得到 l2 的直线方 程. 【答案】D【解析】画出图形,容易求得直线 l1 与 x 轴的交点 A??1,0? ,它关于直线 l 的对称点为 B?5,0? , 又 l1 与 l 的交点 P?2,3? ,从而对称直线 l2 经过 B、P 两点,于是由两点式求得 l2 的方程为 x ? y ? 5 ? 0 . 3. 【命题立意】本题考查两条直线的位置关系和充要条件: l1 ? l2 ? A1 A2 ? B1B2 ? 0 . 【思路点拨】判断直线 l1 : A1 x ? B1 y ? C1 ? 0 , l2 : A2 x ? B2 y ? C2 ? 0 的位置关系时,抓住两点,一是 l1 ∥ l2 时,
A1 B1 C1 ,为了避免讨论系数为零的情况,转化为积式 A1B2 ? A2 B1 且 A1C2 ? A2C1 ;二是 l1 ? l2 ,即斜率 ? ? A2 B2 C2

的乘积为 ?1 ,如果一条直线的斜率为零,则另一条直线的斜率不存在,也就是 A1 A2 ? B1B2 ? 0 .充分必要 条件的判定,关键是看哪个推出哪个. 【答案】A【解析】 l1 ? l2 ? a 2 ? 3a ? 2 ? 0 ? a ? ?1 或 a ? ?2 ,故选答案 A. 4. 【命题立意】本题考查直线与圆的位置关系和点到直线的距离公式以及基本不等式. 【思路点拨】直线与圆的位置关系有三种,由圆心到直线的距离 d 与半径 r 的大小关系决定,当 d>r 时,相离;当 d=r 时相切;当 d<r 时相交. 【答案】D【解析】圆心 ?0,0? 到直线 ax ? by ? a ? b ? 0 的距离 d ?
a?b a ?b
2 2

,半径 r ? 2 .由于 d 2 ?

?a ? b?2 ? 1 ?
a 2 ? b2

2ab a 2 ? b2

?2 ,

所以 d ? r ,从而直线与圆相交或相切. 5. 【命题立意】本题考查直线与圆的位置关系和点到直线的距离. 【思路点拨】圆上的点到直线上的点,这两个动点之间的距离的最小值,可以转化为直线上的点到圆心 的距离的最小值来解决,圆上的点到直线的距离的最大值等于圆心到直线的距离加上半径,最小值等于 圆心到直线的距离减去半径;当直线与圆相交时,圆上的点到直线的距离的最大值等于圆心到直线的距 离加上半径,最小值等于 0.

livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relief a nd development work . Impl em enting poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stations, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack. Poverty alleviati on a nd development li es in pre cise, a ccurate. Pre sent, i n order t o find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepre neurs hip for poverty eradicat ion poverty eradi cation, educati on, poverty all eviation, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by the State Council on furt her pr omoting urba nization constructi on of new opi nions, pro pos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese characteristi cs. A ccor ding t o distri ct -wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dential a nd farm tour towns a nd v illages, f orming one village one product, a feature pattern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted su pport to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of

letters and calls, a nd do pra ctical thi ngs for the ma sses combi ne good, effective thr oug h reaching people at the s ervice of the "last mile". Third, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Jinping stresse d devel opme nt of innovation forest restr uct uring, r evitalizati on of the ol d industrial bases i n Northeast China is the State's maj or strategy, Ce ntral has i ssue d compre hensive opini ons of revitalizing Northea st Chi na and other old i ndustrial bases, t he CPC Ce ntral Committee on revitalization in Nort heast C hina wer e ... V igorous determi nation does not waver, the work does not sla cken off. Be firm with in the development ha s more to do with hard, a nd not muddl e along, pas sive ina ction. To rely on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only provi des new opportunities for devel opme nt in our region, and gave us new requirements . We must s e ize the opportunit y, full use of nati onal poli cy, has to be more compli cated, to start a nd target, give full play to t he initiative of leadi ng cadre s at all levels, a ctive, active, focusing on building ne w moment um for development, a ccel erating t ransformation of forest devel opme nt. To im plement the new development phil os ophy. Phil osophy is t he acti on gui de, new ideas and ne w devel opme nts. Carryi ng out inn ova tion, coor dinati on a nd development of green, open, s hared i deas, m ust be meas urabl e, dire ct action with new development concept s, training cadres . In a new dev elopment concept as a yardstick. E stablis hed i n line with the new conce pt of evaluation system and evaluati on criteri on, embodies t he new deve lopme nt policy, organi zation, mandate im plementati on, always mea sure d by the new dev elopment philosophy, continuous correcti on of forest trans ition course. I n a ne w devel opme nt conce pt for the pat h command. A s part of the impl ementation of the new devel opme nt philosophy followe d and acti on gui deli nes, firmly adjusted, corre cted an d reje ct unsuita ble, ina ppr opriate a nd eve n against the new development i deas, behavi ors and pra ctices , more pragmatic a pproach base d on a broa d visi on, a nd creatively carry out ecologi cal constr uction, i ndustrial devel opme nt, improvi ng pe ople' s livelihood, s uch as the w ork to e nsure t hat new development i deas take root i n forest areas. I n a new development conce pt for weapon traini ng ca dre. Education leaders "in the new, not hing" two arti cles, e nha nci ng vitality and pow er. Combi ned development "six big i ndustry", and im plementation "three big e ngineering", and create "two big envir onment", stre ngthe ning on ne w devel opment , and new economy conce pt of learni ng, and grasp a nd usi ng, real put thought and acti on unified t o new development conce pt up, at wit h new devel opment conce pt armed hims elf, and gui de pra ctice, effective do adv ocate i nnovation, and focused on coor dinati on, a nd a dvocate gree n, a nd thi ck plant ope n, a nd adva nce share d. Second, we must rely on S cience and technology affects. Techni cal innovation is

the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".



【答案】B【解析】由题意可知,直线与圆相离, x 2 ? y 2 ? 4 x ? 4 y ? 7 ? 0 即 ?x ? 2?2 ? ? y ? 2?2 ? 1 ,圆心 ?2,2? 到 直线 y ? kx 的距离 d ?
2k ? 2 k ?1
2

,∴ d ? r ?

2k ? 2 k 2 ?1

? 1 ? 2 2 ? 1 ,解得 k ? ?1 .

6. 【命题立意】考查椭圆的标准方程和椭圆中的基本量及其关系以及分类讨论的思想. 【思路点拨】可建立 m 关于 e 的函数,从而可根据 e 的范围求得 m 的范围. 【答案】C【解析】化椭圆的方程为标准方程 x
2

?

y2 ? 1 ,当 1 1 m m

<1,即 m >1 时,椭圆焦点在 x 轴上,

此时 a 2 ? 1 , b 2 ? < m <2.当

? 3 2? 1 1 1 1 ? ? 3 , c 2 ? 1 ? ,? e 2 ? 1 ? ,? m ? ,又 ? e ? ? 3 , 2 ? ,? < m <2,又 m >1,? 1 2 m m m ? ? 2 1? e

1 1 1 c2 >1,即 m <1 时,椭圆焦点在 y 轴上,此时 a 2 ? , b 2 ? 1 , c 2 ? ? 1 ,∴ e 2 ? 2 ? 1 ? m , m m m a
? 3 2? ? , ? 3 2 ? ?

即 m ? 1 ? e 2 ,又 ? e ? ? ?

,∴

1 2 ?1 2? < m < .综上, m 的范围范围是 ? , ? ? ?1,2? .选择 C. 2 3 ?2 3?

7. 【命题立意】考查双曲线的标准方程,离心率的概念. 【思路点拨】根据渐近线方程可以得到双曲线系方程,再分两种情况讨论焦点位置,从而求得离心率. 【答案】C【解析】由于一条渐近线方程为 3 x ? y ? 0 ,所以可设双曲线方程为 3x 2 ? y 2 ? ? .当焦点在 x 轴上
x2 y2 ? c 4? 时,方程为 ? ? ? ? 1 ( ? >0) ,此时 a 2 ? , b 2 ? ? ,于是 c 2 ? a 2 ? b 2 ? ,所以离心率 e ? ? 2 ;当焦点 3 a 3 3

在 y 轴上时,方程为 ? ? ?
c 2 e ? ? 3 .故选择 C. a 3

y2

x2 ?1 ( ?? 3

? 4? ,此时 a 2 ? ? ? , b2 ? ? ,于是 c 2 ? a 2 ? b 2 ? ? ,所以离心率 ? <0)
3

3

8. 【命题立意】考查抛物线的定义和标准方程以及直角三角形的性质. 【思路点拨】画出图形,利用抛物线的定义找出点 M 的横坐标与|FM|的关系即可求得. 【答案】C【解析】画出图形,知 F?1,0? ,设 FM = 2a ,由点 M 向 x 轴作垂线,垂足为 N,则 FN = a , 于是点 M 的横坐标 x0 ? 1 ? a .利用抛物线的定义,则 M 向准线作垂线,有 FM = x0 ? 1 ,即 2a ? 1? a ?1 , 所以 a ? 2 ,从而 FM =4. 9. 【命题立意】考查椭圆与抛物线的标准方程,基本量的关系以及分类讨论问题. 【思路点拨】由抛物线的标准方程求得准线方程,从而求得椭圆一个顶点的坐标,这个值是 a 还是 b, 就必须分两种情况讨论. 【答案】D【解析】由抛物线 y 2 ? 8 x ,得到准线方程为 x ? ?2 ,又 ? ,即 a ? 2c .当椭圆的焦点在 x 轴上 时,a ? 2 ,c ? 1 ,b 2 ? a 2 ? c 2 ? 3 , 此时椭圆的标准方程为
a?

c a

1 2

x2 y2 ? ?1 ; 当椭圆的焦点在 4 3

y 轴上时,b ? 2 ,c ?

2 3, 3

y2 x2 4 3 ,此时椭圆的标准方程为 16 ? 4 ? 1 .故选择 D. 3 3

10. 【命题立意】考查对向量含义的理解,线段垂直平分线的性质、三角形中位线性质和双曲线定义. 【思路点拨】画出图形,将向量问题转化为实数中线段关系问题,利用线段垂直平分线的性质和三角形 中位线的性质,得到线段的差是常数,符合双曲线的定义. 【答案】B【解析】画出图形, ON ? 1 说明点 N 在圆 x 2 ? y 2 ? 1 上, F1M ? 2 NM 说明 N 是线段 F1 M 的中点, 说明 P 在 MF2 上,F1M ? PN ? 0 说明 PN 是线段 F1 M 的垂直平分线, 于是有 PF1 ? PM , MP ? ? MF2(x∈R)
ON ? 1 MF2 ,从而有 PF1 ? PF2 ? PM ? PF2 ? MF2 ? 2 ON =2< F1F2 =4,所以点 P 的轨迹是以 F1 、 F2 为焦点 2

的双曲线的右支.从而选择 B. 11. 【命题立意】考查圆的方程,直线与圆相切问题. 【思路点拨】圆心已知,故只需求得其半径即可,而半径为圆心(-1,2)到直线的距离,根据点到直线 的距离可求其半径,从而可求得圆的标准方程. 【答案】 ?x ? 1?2 ? ? y ? 2?2 ? 8 【解析】圆的半径 r ?
?1 ? 2 ?1 1 ? ?? 1?
2 2

? 2 2 ,所以圆的方程为 ?x ? 1?2 ? ? y ? 2?2 ? 2 2 2 ,即

? ?

?x ? 1?2 ? ? y ? 2?2 ? 8 .
livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relief a nd development work . Impl ementing poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stations, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack . Poverty alleviati on a nd development li es in pre cise, a ccurate. Pre sent, i n order to find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepre neurs hip for poverty eradication poverty eradi cation, educati on, poverty all eviation, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by th e State Council on furt her pr omoting urba nization constructi on of new opi nions, propos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese characteristi cs. A ccor ding t o distri ct-wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dential a nd farm tour towns a nd v illages, f orming one village one product, a feat ure pattern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted support to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of

letters and calls, a nd do pra ctical t hings for t he masse s com bine g ood, effective through rea chi ng pe ople at the servi ce of the "last mile". T hird, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Ji npi ng stresse d devel opme nt of innovation forest restru cturing, revitalization of the ol d industrial bases i n Northeast Chi na is the State's maj or strategy, Central ha s iss ued compr ehe nsive opi nions of revitalizi ng Nort heast China and other old i ndustrial ba ses, t he CPC Ce ntral Committee on revitalizati on in Nort heast China w ere ... V igorous determination does not waver, the w ork does not sl acken off. Be firm with in the devel opment has more t o do with har d, and not muddle al ong, passiv e ina ction. To re ly on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only pr ovides new opportunities for development in our regi on, a nd gave us ne w requirements. We must s eize the opportunity, full use of national policy, ha s to be m ore com plicate d, to start and target, give full play to t he initiative of leadi ng ca dres at all level s, active, active, focusi ng on building new moment um for devel opment , accelerating t ransformation of forest devel opment . To im plement t he ne w devel opme nt philos ophy. Phi los ophy is the action gui de, new ideas a nd new deve lopme nts. Carry ing out innov ation, coor dinati on a nd development of green, ope n, s hared i deas, must be mea surabl e, dire ct acti on wit h ne w devel opme nt concepts, trai ning ca dres. In a new development concept a s a yardsti ck. Esta blished i n line w ith the new conce pt of evaluati on system a nd eval uation criteri on, embodies the new devel opment poli cy, organizati on, ma ndate im plementation, always mea sure d by the new devel opment phil os ophy, conti nuous correction of forest transition course. In a new development concept for t he pat h comma nd. A s part of the implementati on of the ne w devel opme nt philosophy followe d and acti on gui deli nes, firmly adj usted, cor re cted a nd rej ect uns uitable , ina ppropriate a nd eve n agains t the new devel opment i deas, be haviors a nd practi ces, more pragmatic approa ch base d on a br oad visi on, and creatively carry out e col ogica l construction, industrial devel opme nt, improvi ng pe opl e's liveli hood, such as t he w ork to ensure t hat new devel opment i deas take root in forest area s. I n a new dev elopment concept for wea po n traini ng ca dre. Educati on lea ders "in t he ne w, nothi ng" two articl es, e nha nci ng vitality and power. Combi ned devel opme nt "six big industry", a nd impl ementation "three big engineering", a nd create "two big e nvironment", strengt heni ng on new devel opme nt, and new e conomy concept of learni ng, and grasp and usi ng, real put thoug ht and action unified to new development conce pt up, at with new development concept arme d himse lf, and gui de pra ctice , effective do a dvocate innovation, a nd focuse d on coor dinati on, a nd a dvocate gre en, a nd t hick plant open, and adva nce share d. Second, we must rely on Scie nce a nd te chnol ogy affects. Te chnical innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

12. 【命题立意】考查圆的标准方程,点到直线的距离. 【思路点拨】先化圆的方程为标准方程,求出圆心到直线的距离,再来与半径比较. 【答案】3【解析】圆的方程为 ?x ? 2?2 ? ? y ? 2?2 ? 2 ,圆心 ?2,?2? 到直线 x ? y ? 5 ? 0 的距离 d ? 半径 r ? 2 ,所以圆上到直线的距离等于
2 的点有 3 个. 2
2? 2?5 2 ? 2 ,圆的 2

13. 【命题立意】考查圆心到直线的距离、圆的切线长定理和直线与圆相切问题. 【思路点拨】画出图形,PM 是切线,切线长最小,即|PC|最小,也就是 C 到 l1 的距离. 【答案】 ?1 【解析】画出图形,由题意 l2 与圆 C 只一个交点,说明 l2 是圆 C 的切线,由于 所以要|PM|最小, 只需|PC|最小, 即点 C 到 l1 的距离 PM ? PC ? CM ? PC ? 16 ,
2

2

2

2

2

5?0?3 1 ? m2

?

8 1 ? m2

, 所以|PM|

的最小值为 ?

?

? ? ? 16 ? 4 ,解得 m ? ?1 . ? 2 ? ? 1? m ? 8

14. 【命题立意】考查椭圆的标准方程,椭圆离心率的概念和圆的切线问题. 【思路点拨】画出图形,由椭圆的离心率为 在直角三角形中求解角度.
2 2 c 得到 = ,再利用圆的切线的性质得到直角三角形, 2 2 a

? ? ? sin ?APO ? 2 ? ? 【答案】 【解析】 如图, 连结 OA, 则 OA⊥PA, 所以 ?APO ? , 从而 ?APB ? . a 2 , a 4 2 2
a c c 2

15. 【命题立意】考查双曲线中由 a、b、c 构成的直角三角形的几何意义及离心率与 a、b、c 的关系.[来 源: ] 【思路点拨】可根据四边形的特征,以“有一个内角小于 60°”为桥梁确定离心率的范围. 【答案】 ?
? 6 ? x2 y2 , 2 ? 【解析】设双曲线的方程为 2 ? 2 ? 1 =1(a>0,b>0),如图所示,由于在双曲线 c> ? 2 ? a b ? ?

b,所以只能是 ?B1F1B2 <90° ,故由题意可知 60° < ?B1F1B2 <90° , ∴在 Rt?OF1B1 中,30° < ?OF1B1 <45° ,∴ 即
3 2 c2 ? a2 b 1 1 < < ,∴ < < , 3 2 c 3 2 c2

1 6 1 1 3 <1- 2 < ,∴ <e2<2,∴ <e< 2 . 2 3 2 2 e

16. 【命题立意】考查圆的标准方程,直线与圆的位置关系,以及弦长问题. 【思路点拨】 (1)过圆外一点的圆的切线方程,一般设斜率,利用圆心到直线的 距离等于半径来求出斜率,但一定要注意斜率存在与否; (2)将弦长 AB 看成底 边,则三角形的高就是圆心到直线的距离. 【解析】 (1)圆心为 O?0,0? ,半径 r ? 4 ,当切线的斜率存在时,设过点 M ??4,8? 的 切线方程为 y ? 8 ? k ?x ? 4 ? , 即 kx ? y ? 4k ? 8 ? 0(1 分) . 则
| 4k ? 8 | k 2 ?1 ? 4, 解得 k ? ?
3 , 4

(3 分) ,于是切线方程为 3x ? 4 y ? 20 ? 0(5 分) .当斜率不存在时, x ? ?4 也符合题意.故过点 M ??5,11? 的 圆 O 的切线方程为 3x ? 4 y ? 20 ? 0 或 x ? ?4 . (6 分) (2)当直线 AB 的斜率不存在时, S ?ABC ? 3 7 , (7 分) ,当直线 AB 的斜率存在时, 设直线 AB 的方程为 y ? k ?x ? 3? ,即 kx ? y ? 3k ? 0 ,圆心 O?0,0? 到直线 AB 的距离
d? 3k k 2 ?1

, (9 分)线段 AB 的长度 AB ? 2 16 ? d 2 ,所以

S?ABC ?
9k 2 k 2 ?1

1 d 2 ? 16 ? d 2 2 AB d ? d 16 ? d 2 ? d 2 16 ? d 2 ? ?8, (11 分)当且仅当 d 2 2

?

?

?

?

? 8 时取等号,此时

? 8 ,解得 k ? ?2 2 ,所以 △ (12 分) OAB 的最大面积为 8,此时直线 AB 的斜率为 ? 2 2 .

17.【命题立意】本题考查椭圆方程的求法,直线和圆锥曲线的位置关系以及存在性问题. 【思路点拨】 (1)可根据抛物线平移后与坐标轴的交点求得 b 、 c 的值,从而可得 a 的值,故可求椭圆 方程; (2)可利用向量法解决.

livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relief a nd development work . Impl em enting poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stations, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack. Poverty alleviati on a nd development li es in pre cise, a ccurate. Pre sent, i n order t o find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepre neurs hip for poverty eradicat ion poverty eradi cation, educati on, poverty all eviation, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by the State Council on furt her pr omoting urba nization constructi on of new opi nions, pro pos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese characteristi cs. A ccor ding t o distri ct -wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dential a nd farm tour towns a nd v illages, f orming one village one product, a feature pattern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted su pport to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of

letters and calls, a nd do pra ctical thi ngs for the ma sses combi ne good, effective thr oug h reaching people at the s ervice of the "last mile". Third, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Jinping stresse d devel opme nt of innovation forest restr uct uring, r evitalizati on of the ol d industrial bases i n Northeast China is the State's maj or strategy, Ce ntral has i ssue d compre hensive opini ons of revitalizing Northea st Chi na and other old i ndustrial bases, t he CPC Ce ntral Committee on revitalization in Nort heast C hina wer e ... V igorous determi nation does not waver, the work does not sla cken off. Be firm with in the development ha s more to do with hard, a nd not muddl e along, pas sive ina ction. To rely on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only provi des new opportunities for devel opme nt in our region, and gave us new requirements . We must s e ize the opportunit y, full use of nati onal poli cy, has to be more compli cated, to start a nd target, give full play to t he initiative of leadi ng cadre s at all levels, a ctive, active, focusing on building ne w moment um for development, a ccel erating t ransformation of forest devel opme nt. To im plement the new development phil os ophy. Phil osophy is t he acti on gui de, new ideas and ne w devel opme nts. Carryi ng out inn ova tion, coor dinati on a nd development of green, open, s hared i deas, m ust be meas urabl e, dire ct action with new development concept s, training cadres . In a new dev elopment concept as a yardstick. E stablis hed i n line with the new conce pt of evaluation system and evaluati on criteri on, embodies t he new deve lopme nt policy, organi zation, mandate im plementati on, always mea sure d by the new dev elopment philosophy, continuous correcti on of forest trans ition course. I n a ne w devel opme nt conce pt for the pat h command. A s part of the impl ementation of the new devel opme nt philosophy followe d and acti on gui deli nes, firmly adjusted, corre cted an d reje ct unsuita ble, ina ppr opriate a nd eve n against the new development i deas, behavi ors and pra ctices , more pragmatic a pproach base d on a broa d visi on, a nd creatively carry out ecologi cal constr uction, i ndustrial devel opme nt, improvi ng pe ople' s livelihood, s uch as the w ork to e nsure t hat new development i deas take root i n forest areas. I n a new development conce pt for weapon traini ng ca dre. Education leaders "in the new, not hing" two arti cles, e nha nci ng vitality and pow er. Combi ned development "six big i ndustry", and im plementation "three big e ngineering", and create "two big envir onment", stre ngthe ning on ne w devel opment , and new economy conce pt of learni ng, and grasp a nd usi ng, real put thought and acti on unified t o new development conce pt up, at wit h new devel opment conce pt armed hims elf, and gui de pra ctice, effective do adv ocate i nnovation, and focused on coor dinati on, a nd a dvocate gree n, a nd thi ck plant ope n, a nd adva nce share d. Second, we must rely on S cience and technology affects. Techni cal innovation is

the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".



【解析】 (1)抛物线 x 2 ? ?2 2 y 的图象向上平移 2 个单位长度后其解析式为 x 2 ? ?2 2 y ? 2 ,其与 x 、 ∴ b ? 2 ,c ? 2 , (2 分) ∴ a2 ? 6 , 故椭圆的方程为 y 轴的交点坐标分别为 ??2,0? 、 0, 2 , 分) (2)由题意可得直线 l 的方程为 y ? ?
3 ?x ? m? ,代入椭圆方程消去 3

?

?

? ?

x2 y2 ? ?1 . (4 6 2

(6 分) y 得, 2 x 2 ? 2mx ? m 2 ? 6 ? 0 ,

又 △? 4m 2 ? 8 m 2 ? 6 >0,∴ ? 2 3 < m < 2 3 . (7 分)设 C、D 分别为 ?x1, y1? , ?x2 , y 2 ? ,则 x1 ? x2 ? m ,
x1x2 ?
? 3 ? ? 3 ? 1 m m2 m2 ? 6 , ∴ y1 y2 ? ?? ?x1 ? m ?? ? ?? ?x2 ? m ?? ? x1x2 ? ?x1 ? x2 ? ? , ∵ FC ? ?x1 ? 2, y1 ? , FD ? 3 3 2 ? ? ? ? 3 ? ? ? 3 ? 3

?

?

?x2 ? 2, y2 ? ,

∴ FC ? FD ? ?x1 ? 2??x2 ? 2? ? y1 y2 ? x1x2 ?
FC ? FD >0,即

4 3

2 m?6 (10 分)∵点 F 在圆的外部,∴ ?x1 ? x2 ? ? m ? 4 ? 2m?m ? 3? , 3 3 3

2 m ?m ? 3? >0,解得 m <0 或 m >3,又∵ ? 2 3 < m < 2 3 ,∴ ? 2 3 < m <0 或 3< m 3

< 2 3 .(12 分) 18.【命题立意】考查双曲线的定义和标准方程,渐近线和离心率计算公式. 【思路点拨】 (1)求渐近线方程的目标就是求 b ,可根据条件建立 a、b 的数量关系来求得; (2)可建立 e
a

关于 ? 的函数,从而可根据 ? 的范围求得 e 的范围; (3)可根据离心率确定 a、b 的数量关系,再结合图形 确定圆的圆心与半径. 【解析】由于 F2 ?c,0? ,所以 P? c,? b ? ,于是 PF2 ?
2

? ? ?

? a ? ?

2 b2 , PF1 ? PF2 ? 2a ? b ? 2a , (1 分)由相似三角形知, a a

OH PF2

?

OF1 PF1

,即

OH OF1

?

PF2 PF1

,即 ? ?

b2 a b 2a ? a
2

, (2 分)∴ 2a 2 ? ? b 2 ? ? b 2 , 2a 2? ? b 2 ?1 ? ? ? ,

b2 a2

?

2? . 1? ?

(1)当 ? ? (2) e2 ? ∴当 ? ? 分)

1 b2 时, 2 ? 1 ,∴ a ? b . (3 分)所以双曲线的渐近线方程为 y ? ?x . (4 分) 3 a
2

c2 a

? 1?

b2 a2

? 1?

2? 2?1 ? ?1 ? ? ?? 2 2 ?1 1 ? ,在 ? , ? 上为单调递增函数. (5 分) ? 1? ? ? 1 ? ?1 ? 1? ? 1? ? 1? ? ? ?1 ?9 2?

1 1 5 5 5 2 ?e? 3 . 时,e 2 取得最大值 3 (6 分) ; 当 ? ? 时,e 取得最小值 . (7 分) ∴ ? e2 ? 3 , ∴ (8 2 9 4 2 4

(3)当 e ? 3 时, ? 3 ,∴ c ? 3 a ,∴ b 2 ? 2a 2 . (9 分)∵ PF2 ? F 1 是圆的直径,圆心是 PF 1 1F 2 ,∴ PF 的中点, ∴在 y 轴上截得的弦长就是直径, ∴ PF1 ? 8 . (10 分) 又 PF1 ? 2a ?
c ? 2 3 ,b ? 2 2 . (11 分) ∴ PF2 ?

c a

b2 2a 2 ∴ 4a ? 8 ,a ? 2 , ? 2a ? ? 4a , a a

b2 ? 2a ? 4 , 圆心 C?0,2? , 半径为 4, 故圆的方程为 x 2 ? ? y ? 2?2 ? 16 . (12 a

分) 19.【命题立意】考查抛物线的标准方程,直线与抛物线的位置关系. 【思路点拨】设直线方程,与抛物线方程联立,利用韦达定理来解决;存在性问题一般是假设存在,利 用垂径定理推导求解来解决. 【解析】 (1)依题意,可设 A?x1, y1? 、 B?x2 , y2 ? ,直线 AB 的方程为 x ? my ? p ,

livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relief a nd development work . Impl ementing poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stations, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack . Poverty alleviati on a nd development li es in pre cise, a ccurate. Pre sent, i n order to find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepre neurs hip for poverty eradication poverty eradi cation, educati on, poverty all eviation, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by th e State Council on furt her pr omoting urba nization constructi on of new opi nions, propos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese characteristi cs. A ccor ding t o distri ct-wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dential a nd farm tour towns a nd v illages, f orming one village one product, a feat ure pattern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted support to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of

letters and calls, a nd do pra ctical t hings for t he masse s com bine g ood, effective through rea chi ng pe ople at the servi ce of the "last mile". T hird, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Ji npi ng stresse d devel opme nt of innovation forest restru cturing, revitalization of the ol d industrial bases i n Northeast Chi na is the State's maj or strategy, Central ha s iss ued compr ehe nsive opi nions of revitalizi ng Nort heast China and other old i ndustrial ba ses, t he CPC Ce ntral Committee on revitalizati on in Nort heast China w ere ... V igorous determination does not waver, the w ork does not sl acken off. Be firm with in the devel opment has more t o do with har d, and not muddle al ong, passiv e ina ction. To re ly on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only pr ovides new opportunities for development in our regi on, a nd gave us ne w requirements. We must s eize the opportunity, full use of national policy, ha s to be m ore com plicate d, to start and target, give full play to t he initiative of leadi ng ca dres at all level s, active, active, focusi ng on building new moment um for devel opment , accelerating t ransformation of forest devel opment . To im plement t he ne w devel opme nt philos ophy. Phi los ophy is the action gui de, new ideas a nd new deve lopme nts. Carry ing out innov ation, coor dinati on a nd development of green, ope n, s hared i deas, must be mea surabl e, dire ct acti on wit h ne w devel opme nt concepts, trai ning ca dres. In a new development concept a s a yardsti ck. Esta blished i n line w ith the new conce pt of evaluati on system a nd eval uation criteri on, embodies the new devel opment poli cy, organizati on, ma ndate im plementation, always mea sure d by the new devel opment phil os ophy, conti nuous correction of forest transition course. In a new development concept for t he pat h comma nd. A s part of the implementati on of the ne w devel opme nt philosophy followe d and acti on gui deli nes, firmly adj usted, cor re cted a nd rej ect uns uitable , ina ppropriate a nd eve n agains t the new devel opment i deas, be haviors a nd practi ces, more pragmatic approa ch base d on a br oad visi on, and creatively carry out e col ogica l construction, industrial devel opme nt, improvi ng pe opl e's liveli hood, such as t he w ork to ensure t hat new devel opment i deas take root in forest area s. I n a new dev elopment concept for wea po n traini ng ca dre. Educati on lea ders "in t he ne w, nothi ng" two articl es, e nha nci ng vitality and power. Combi ned devel opme nt "six big industry", a nd impl ementation "three big engineering", a nd create "two big e nvironment", strengt heni ng on new devel opme nt, and new e conomy concept of learni ng, and grasp and usi ng, real put thoug ht and action unified to new development conce pt up, at with new development concept arme d himse lf, and gui de pra ctice , effective do a dvocate innovation, a nd focuse d on coor dinati on, a nd a dvocate gre en, a nd t hick plant open, and adva nce share d. Second, we must rely on Scie nce a nd te chnol ogy affects. Te chnical innovation is the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".

由? ?

? y1 ? y2 ? 2 pm (2 分)得 ? , (3 分)∴ ? y 2 ? 2 pmy ? 2 p2 ? 0 , ? 2 ? ? ? y ? 2 px ? y1 ? y2 ? ?2 p ?x ? my ? p
2

NA ? NB = ?x1 ? p, y1 ??x2 ? p, y2 ?

? ?x1 ? p ??x2 ? p ? ? y1 y 2

2 ? ?my1 ? 2 p ??my2 ? 2 p ? ? y1 y2 ? m2 ? 1 y1 y2 ? 2 pm? y1 ? y2 ? ? 4 p 2 ? 2 p 2 m 2 ? 2 p( NA ? NB 取得最小值 2 p 2 . 6 分) 当 m ? 0 时,

?

?

(7 分) (2)假设满足条件的直线 l 存在,其方程为 x ? a ,AC 的中点为 O? ,l 与以 AC 为直径的圆相交于 P、Q, PQ 的中点为 H,则 O?H ? PQ , O? 的坐标为 ? ?
? PH
2

x1 ? p y1 ? , ? .? O?P ? 1 AC ? 1 2 2 2 ? ? 2

?x1 ? p ?2 ? y12

?

1 x12 ? p 2 2

(9 分) ,
?

? O?P ? O?H ?

2

2

2 1 2 1 1 ? ? x1 ? p 2 ? ?2a ? x1 ? p ?2 ? ? a ? p ? x1 ? a? p ? a ? , PQ = 2 PH 4 4 2 ? ?

?

?

?

1 ? ? ? a ? p ? x1 ? a? p ? a ?? ?2 = 4? 2 ? ?? ?

?

(11 分) , 令a? 分)

1 1 1 p?0 得a ? p. 此时 PQ ? p 为定值. 故满足条件的直线 l 存在, 其方程为 x ? p . (13 2 2 2

20.【命题立意】考查椭圆与抛物线的标准方程,直线与椭圆的位置关系. 【思路点拨】 (1)利用抛物线的标准方程,求出焦点坐标,从而得到椭圆中的 b,再由离心率建立方程,可求 得椭圆的标准方程; (2)抓住直线 PQ⊥x 轴, ?APQ ? ?BPQ 即直线 PA、PB 的斜率互为相反数,联系方程 利用韦达定理来解决. 【解析】 (1)设 C 方程为
x2 a
2

?

y2 b2

? 1 (a>b>0) ,则 b ? 2 3

.由

c 1 ? a 2

, a 2 ? c 2 ? b 2 ,得 a=4∴椭圆 C 的

2 2 1 x2 y2 ?1 , 方程为 x ? y ? 1 . (4 分) (2)①设 A? x1 , y1 ? , B?x2 , y2 ? ,直线 AB 的方程为 y ? x ? t ,代入 ?

16

12

2

16

12

得 x 2 ? tx ? t 2 ? 12 ? 0 ,由 ? >0,解得 ?4 < t <4. (6 分)由韦达定理得 x1 ? x2 ? ?t , x1 x2 ? t 2 ? 12 . 四边形 APBQ 的面积 S ?
1 ? 6 ? x1 ? x2 ? 3 48 ? 3t 2 ,∴当 t 2

? 0 时 S max

? 12 3 . (8 分)

②当 ?APQ ? ?BPQ ,则 PA、PB 的斜率之和为 0,设直线 PA 的斜率为 k ,则 PB 的斜率为 ?k ,PA 的直 线方程为 y ? 3 ? k ?x ? 2 ? ,由 ? ? x2
8?2k ? 3?k 3 ? 4k
2

? y ? 3 ? k ?x ? 2?(1) y2 ? 1(2) ? ? ? 16 12

.将(1)代入(2)整理得 3 ? 4k 2 x 2 ? 8?3 ? 2k ?kx ? 4?3 ? 2k ?2 ? 48 ? 0 ,
?8k ??2k ? 3? 3 ? 4k
2

?

?

有 x1 ? 2 ? ∴ x1 ? x2 ?

. (10 分)同理 PB 的直线方程为 y ? 3 ? ?k(x ? 2) ,可得 x2 ? 2 ?
?48k 3 ? 4k 2

?

8k ?2k ? 3? 3 ? 4k 2



16k 2 ? 12 3 ? 4k 2

,x1 ? x2 ?

. (12 分) 从而 k AB =

y1 ? y 2 k ?x ? 2? ? 3 ? k ?x2 ? 2? ? 3 k ?x1 ? x2 ? ? 4k 1 = 1 = = , x1 ? x2 x1 ? x2 x1 ? x2 2

所以 AB 的斜率为定值

1 . (13 分) 2

21.【命题立意】考查圆锥曲线的标准方程,椭圆与双曲线的定义,向量垂直问题. 【思路点拨】 (1)利用向量的数量积的坐标运算来求出轨迹方程,但一定要注意对参数的讨论; (2)利 用椭圆或双曲线的定义确定点 P 的位置,以 PQ 为直径的圆 G 过点 F2 ,即 PF2 ? QF2 ? 0 ,利用向量垂直 的坐标运算来解决. 【解析】 (1)∵ a ? b ,∴ a ? b ? ?x, y ? 2? ? ?kx, y ? 2? ? 0 ,得 kx 2 ? y 2 ? 4 ? 0 ,即 kx 2 ? y 2 ? 4 . (1 分)

livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relief a nd development work . Impl em enting poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stations, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack. Poverty alleviati on a nd development li es in pre cise, a ccurate. Pre sent, i n order t o find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepre neurs hip for poverty eradicat ion poverty eradi cation, educati on, poverty all eviation, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by the State Council on furt her pr omoting urba nization constructi on of new opi nions, pro pos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese characteristi cs. A ccor ding t o distri ct -wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dential a nd farm tour towns a nd v illages, f orming one village one product, a feature pattern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted su pport to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of

letters and calls, a nd do pra ctical thi ngs for the ma sses combi ne good, effective thr oug h reaching people at the s ervice of the "last mile". Third, foster t he devel opme nt of new e nergy, new G eneral Se cretary XI Jinping stresse d devel opme nt of innovation forest restr uct uring, r evitalizati on of the ol d industrial bases i n Northeast China is the State's maj or strategy, Ce ntral has i ssue d compre hensive opini ons of revitalizing Northea st Chi na and other old i ndustrial bases, t he CPC Ce ntral Committee on revitalization in Nort heast C hina wer e ... V igorous determi nation does not waver, the work does not sla cken off. Be firm with in the development ha s more to do with hard, a nd not muddl e along, pas sive ina ction. To rely on t heir ow n efforts, ca n't wait, ca n't wait, stand still. T his not only provi des new opportunities for devel opme nt in our region, and gave us new requirements . We must s e ize the opportunit y, full use of nati onal poli cy, has to be more compli cated, to start a nd target, give full play to t he initiative of leadi ng cadre s at all levels, a ctive, active, focusing on building ne w moment um for development, a ccel erating t ransformation of forest devel opme nt. To im plement the new development phil os ophy. Phil osophy is t he acti on gui de, new ideas and ne w devel opme nts. Carryi ng out inn ova tion, coor dinati on a nd development of green, open, s hared i deas, m ust be meas urabl e, dire ct action with new development concept s, training cadres . In a new dev elopment concept as a yardstick. E stablis hed i n line with the new conce pt of evaluation system and evaluati on criteri on, embodies t he new deve lopme nt policy, organi zation, mandate im plementati on, always mea sure d by the new dev elopment philosophy, continuous correcti on of forest trans ition course. I n a ne w devel opme nt conce pt for the pat h command. A s part of the impl ementation of the new devel opme nt philosophy followe d and acti on gui deli nes, firmly adjusted, corre cted an d reje ct unsuita ble, ina ppr opriate a nd eve n against the new development i deas, behavi ors and pra ctices , more pragmatic a pproach base d on a broa d visi on, a nd creatively carry out ecologi cal constr uction, i ndustrial devel opme nt, improvi ng pe ople' s livelihood, s uch as the w ork to e nsure t hat new development i deas take root i n forest areas. I n a new development conce pt for weapon traini ng ca dre. Education leaders "in the new, not hing" two arti cles, e nha nci ng vitality and pow er. Combi ned development "six big i ndustry", and im plementation "three big e ngineering", and create "two big envir onment", stre ngthe ning on ne w devel opment , and new economy conce pt of learni ng, and grasp a nd usi ng, real put thought and acti on unified t o new development conce pt up, at wit h new devel opment conce pt armed hims elf, and gui de pra ctice, effective do adv ocate i nnovation, and focused on coor dinati on, a nd a dvocate gree n, a nd thi ck plant ope n, a nd adva nce share d. Second, we must rely on S cience and technology affects. Techni cal innovation is

the promoti on of economi c transformation and upgra ding, quality a nd efficie ncy "first pow er".



当 k ? 0 时,方程表示两条与 x 轴平行的直线; (2 分)当 k ? 1 时,方程表示以原点为圆心,以 2 为半径 的圆; (3 分)当 0< k <1 时,方程表示焦点在 x 轴上的椭圆; (4 分)当 k >1 时,方程表示焦点在 y 轴 上的椭圆; (5 分) 当 k <0 时,方程表示焦点在 y 轴上的双曲线. (6 分)
y2 x2 ? ?1 , 则 F1 、 解法一: 由椭圆定义得 PF1 ? PF2 ? 4 , F2 为椭圆的两焦点. 4 3 5 3 2 2 2 联立 PF1 ? PF2 ? 1 解得 PF1 ? , PF2 ? ,又 F1F2 ? 2 ,有 PF1 ? PF2 ? F1F2 ,∴ PF2 ? F 1F 2 ,∴P 的 2 2

(2) 由 (1) 知, 轨迹 T 是椭圆

纵坐标为 1,把 y ? 1 代入

3 3 y2 x2 ?3 ? ? ? 1 得 x ? 或 x ? ? (舍去) ,∴ P? ,1? . (9 分)设存在满足条件的圆, 2 2 4 3 ?2 ?

则 PF2 ? QF2 ,设 Q ?s, t ? ,则 PF2 ? ? ? ,0 ? , QF2 ? ?? s,1 ? t ? ,∴ PF2 ? QF2 ? 0 ,即 s ? 0 ? ?1 ? t ? ? 0 ,∴ s ? 0 .又
? 3 ? 2 ? ?
3 2
2 2 t 2 s2 3? ? 3? 13 或 ? ? 1 ,∴ t ? ?2 ,∴ Q?0,2? 或 Q?0,?2? . (12 分)所以圆 G 的方程: ? ?x? ? ?? y ? ? ? 4 3 4? ? 2? 16 ?

3? ? 1? 45 . ? (13 ?x? ? ?? y ? ? ? 4? ? 2? 16 ?

2

2

分)

livelihood, i s related to people's w ell-being a nd social harmony and stabilit y. We need t o prote ct and improve the livelihood of the people as the starting point a nd e ndi ng point of transiti on a nd impr ove forest pe ople' s feeling and ha ppi nes s. To prom ote poverty relief a nd development work . Impl ementing poverty alleviation cr ucial proje ct is a major strategi c de cisi on made by the CPC Central Committee, is als o determine d by the provi ncial "first project", we must unify thi nking a nd a ction to the re quireme nts of the Central, pr ovincial, res olutely wi n the poverty battle. T he previ ous phase I to 18 stations, Tahe, Pine Ri dge research, visite d many of the poor, go, the heavie r, more pre ssur e. For poverty relief and development w ork, we must pay attention t o it, always in mi nd, gras ping hands, s hould not be blindly optimistic, t here ca n be no s lack . Poverty alleviati on a nd development li es in pre cise, a ccurate. Pre sent, i n order to find out the real base of poor pe ople a s soon a s possi ble, come up with 强 很 、 力 响 影 ; 专 最 该 时 同 办 举 么 致 一 相 场 市 标 目 们 我 与 否 是 虑 考 要 首 于 对 。 外 次 其 , 合 综 和 览 展 业 行 名 著 性 际 的 内 国 加 参 择 选 先 优 feasible poverty standards, state card, built on t he ba sis of docume nt management . To firmly establis h the " poverty reducti on" concept, increase t he inte nsity of res our ce integration, a nd relate d funding, with limite d funds wi sely. By usi ng a combi nation of empl oyment, e ntrepre neurs hip for poverty eradication poverty eradi cation, educati on, poverty all eviation, medi cal aid of poverty means, due to effects of poli cies, those poli cies, e ns ure the com pletion of missi on obj ectives for poverty eradicati on for t he year. To actively promote t he constr ucti on of new t owns. I n February t his yea r, promulgate d by th e State Council on furt her pr omoting urba nization constructi on of new opi nions, propos ed to a dhere to t he people-centere d, four moder nizati ons synchronizati on, optimizati on, e col ogy civ ilization and cultural heritage of new urba nization pat h with Chi nese characteristi cs. A ccor ding t o distri ct-wi de constructi on of civiliz ed city and the beautif ul country side, f urther stre ngthe ning of urba n transport, water supply a nd drainage a nd sewage, waste dis posal ground, underground, s uch as infrastructure construction, strive to create a safer and m ore livable environment. To a ctively seize t he full st op a nd opportunities for poverty alleviation and dev elopment, further efforts to increa se forest villages merge, population to the County (distri ct) Council sites a nd centre s concentrated i n villages a nd towns . Com bine d devel opme nt of urban constructi on a nd t ourism i ndustries, careful pla nni ng and constr ucti on of a number of suita ble for resi dential a nd farm tour towns a nd v illages, f orming one village one product, a feat ure pattern. Closer to the ma sses. Si nce last year, our i n-dept h implementati on of the leadi ng ca dres of grassr oots mas ses at w ork, solve t he pr oblem s of a large number of people, get the mas ses give w hole hearted support to and prais e, this w ork will carry on, abs olutely cannot or movement. Grassroots masse s and ca dres in com bination wit h poverty re duction, com bine d with the stea dy work of


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