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解答题 | 较难(0.4) | 2021·全国高三其他模拟(理)
解题方法
1 . 过直线y=﹣1上动点M,作抛物线eqId4cb5b1f296dd4d329771895d2608ff9b的切线MAMBAB为切点,∠AMB=90°.
(1)求抛物线方程;
(2)若△MAB面积为32,求直线AB的斜率.
解答题 | 一般(0.65) | 2021·浙江高二期末
2 . 已知抛物线eqIdd050af449075401299cc78c647d310e8的焦点为F,过点F的直线eqId417e80f1349244878d01fe90e0891f5f与该抛物线交于AB两点,Ax轴的上方,圆eqId4677430a496d48619e670b11d4e4cf43
说明: figure
(1)若eqId5ca6b76bcfe642d8874c900b49dba3ec,求点A的坐标;
(2)若直线l与圆C相切,求弦eqId99a3187c2b8f4bcc9703c74c3b72f1f3的长;
(3)若直线l与圆C交于MN两点,eqId141aacd92be1460fbdf80d5753578ae0eqId5dd61720ae9e4001a66dda87c9ee71df的面积分别记为eqIde0b0a69153d74086acac0f2b28878deceqIdc36de5c6d722440e9911d9802c4068f8,求eqId3890a25f61ac42d5a7c9934d334a7b51的取值范围.
更新:2021/06/14组卷:0
解答题 | 一般(0.65) | 2021·浙江金华市·高三三模
解题方法
3 . 已知抛物线C的方程为eqId294af0137a7a4b2f873817ba8fbafb44,它的焦点F到点M eqId43f48c7433a8497aa02549d2ed50f0ce的距离为eqIdad04b6cca48b47cdbd0d239142650251.
说明: figure
(1)求抛物线C的方程;
(2)ABD是抛物线C上不同三点,且△ABD是以B为直角顶点的等腰直角三角形,求eqId79a57088b7d245009382342be2e9e22d的最小.
解答题 | 一般(0.65) | 2021·浙江高二期末
解题方法
4 . 已知抛物线eqId1b366c99fef542a49bff5d631ac817ce,其焦点为F,抛物线上有相异两点eqIde8e523c405ae45c19676ed23f0cef311eqId55cba36c462f4746af6690bf1ac89881
说明: figure
(1)若eqIdc7e3411e41de449295daf92a88bbb152轴,且经过点A的抛物线的切线经过点eqId8ee3687f973c472aa424869ab39903eb,求抛物线方程;
(2)若eqId10733093f7274b47abdf247b093a0d5b,且eqIda3ab03dfa0a54af0af0fd3cf704f4c0b,线段AB的中垂线交x轴于点C,求eqId64b9b599fdb6481e9f8d9a94c102300b面积的最大值.
更新:2021/06/13组卷:0
5 . 在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,椭圆eqId15bfbddeee0143e08c809ecf76ffb129的离心率为eqId49b7b111d23b44a9990c2312dc3b7ed9,过椭圆右焦点F作两条互相垂直的弦eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqId34c6b6e427744abfb88dc90b8c7c2111.当直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3斜率为0时,eqId76506bf6b8b6420b9affc7fb39b26b35
(1)求椭圆的方程;
(2)求四边形eqId8cb5c539b00f4c198d985dd69d29e0b5面积的最小值.
解题方法
压轴
6 . 已知抛物线eqId700a7a31089a42d792d3bec553706bf5和右焦点为F的椭圆eqId95f367d34aff4640a83a25c285f425d1.如图,过椭圆eqId3a63d00111554b9e8b896929779a293d左顶点T的直线交抛物线eqIdcfc8599bedfb4ab4944abf141f348a9aAB两点,且eqId2af8d163efa84d6c809109d8f0a3d0df.连接AFeqId3a63d00111554b9e8b896929779a293d于两点MN,交eqIdcfc8599bedfb4ab4944abf141f348a9a于另一点C,连BCQBC的中点,TQACD
说明: figure
(1)证明:点A的横坐标为定值;
(2)记eqId98cbec6d769e4396962dc8340cb76416eqIdedbb25b3d65c45ce9a989d9781f765a2的面积分别为eqIde0b0a69153d74086acac0f2b28878deceqIdc36de5c6d722440e9911d9802c4068f8,若eqIdfed055739f0d48f191d12dcbb57713e8,求抛物线的方程.
解答题 | 较难(0.4) | 2021·重庆高三三模
解题方法
压轴
7 . 已知圆eqId3d8248cac5f44a6f88ca156f23cc7b75和点eqId1b573006a4194630bf3b46bc849dd766,动圆eqId2381423d4cd146cab95f55527681a766经过点eqId63db14a5b4334f3ea583c8fb12b0d175,且与圆eqId93cbffaa5ae045d6ac45d1e979991c3a内切.
(1)求动圆的圆心eqId2381423d4cd146cab95f55527681a766的轨迹eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)设点eqId27def10acc1d4a29ac2d6bedcfa2ebc4关于点eqId63db14a5b4334f3ea583c8fb12b0d175的对称点为eqId7646787b00ab4b69b9f0316d7b7a3ed0,直线eqIdb9dea9bb075e405ba7311b6727a43a2e与轨迹eqId19a4eb16029e4550a14f2afe4741a3c3交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,若eqId1d86496a672b433599927de4de68ed90的面积为eqIdbc83c0c2b3ee474da13554226394e720,求eqId69f56ef2c88b4b73a560da59f5247a82的值.
解答题 | 较难(0.4) | 2021·浙江高三其他模拟
解题方法
压轴
8 . 已知点eqId63db14a5b4334f3ea583c8fb12b0d175为抛物线eqId19a4eb16029e4550a14f2afe4741a3c3eqId38424d93ea714761a9c5264ba5127bb5的焦点,点eqId2f99e09645b24f0984e8af86b59173b4,点eqId052844cae8574a8ab842c38a039baac0为抛物线eqId19a4eb16029e4550a14f2afe4741a3c3上的动点,直线eqId417e80f1349244878d01fe90e0891f5feqIddf1a025b5c5342cfab59c5da249f5b23截以eqId8a76bbe21fb549e3a9c2038d58c7a3d8为直径的圆所得的弦长为定值.
说明: figure
(1)求eqId69f56ef2c88b4b73a560da59f5247a82的值;
(2)如图,直线eqId417e80f1349244878d01fe90e0891f5feqId072d7d6b911b42bc89207e72515ebf5f轴于点eqId93cbffaa5ae045d6ac45d1e979991c3a,抛物线eqId19a4eb16029e4550a14f2afe4741a3c3上的点eqId8754ce8cf7f34f04abb9a0c041f57f5c满足eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中垂线过点eqId0cd8063abf2b458f80091bc51b75a904且直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3不与eqIda9cd3f94eb8045438f75e9daccfa7200轴平行,求eqIde3b69153b86748958fa330bb5aa15e15的面积的最大值.
单选题 | 一般(0.65) | 2020·全国高三其他模拟(文)
解题方法
9 . 已知F是椭圆eqId1f2c4f36fc90433e8c7fb977bad97345的下焦点,过点F的直线l与椭圆交于AB两点,O为坐标原点,则eqIddf1261303406416b95167db34b378716面积的取值范围是(   )
A.eqIdb8c6753cb0a0447788c417ed8b177129B.eqId217ffc15e64b4d10838408bb6e99c0ceC.eqId70e6c3520a51468489b383b5919ec8b7D.eqIde734e51201474f58b633ca4b608d513b
10 . 如图所示,已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId9026e6d24e404bb2808fe83705f83954的离心率为eqIde4d58f42bad9461b93d451da718fc6f4,且过点eqId256fccabecb24a9991a23ee393ced631
说明: figure
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)设eqId75a143b898e14ccdb032561fba9da811在椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上,且eqId0743582db60f420c9cae978529e721bbeqIda9cd3f94eb8045438f75e9daccfa7200轴平行,过eqIdb0e26931f4074788abdc767b79f43e51作两条直线分别交椭圆eqId19a4eb16029e4550a14f2afe4741a3c3于两点eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c,直线eqId0743582db60f420c9cae978529e721bb平分eqIde1d84b54e01a4f909660cb3bddc6eff9,且直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3过点eqId4bdf652a3fbd484fb7af8756d03065c4,求四边形eqIde1fccaf4c050498ea7d81934a8f6c1a0的面积.
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