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解答题 | 一般(0.65) | 2021·全国高三专题练习
解题方法
1 . 如图所示,设抛物线CeqId1aacfd8f79754517ab57903022e76d98的焦点为F,动点P在直线leqIdc14739b2ae5b4fde972e08210a7f67d5上运动,过P作抛物线C的两条切线eqIdd3a908032e2b40df95a6d86089b3f682eqId0fd9ac73d66042c6bbd74f8ccdcbd9fc,切点分别为AB,求证:eqId489de832efac484aaa37885c50fbd041.
说明: figure
解答题 | 一般(0.65) | 2021·贵州(文)
2 . 已知椭圆CeqId15bfbddeee0143e08c809ecf76ffb129的离心率为eqId5f816d038c584dc7a249120298677ef3,直线l经过椭圆C的右焦点F与上顶点,原点O到直线l的距离为eqId5f816d038c584dc7a249120298677ef3.
(1)求椭圆C的方程;
(2)斜率不为0的直线n过点F,与椭圆C交于MN两点,若椭圆C上一点P满足eqId4658c5b128e1451fb85b20e487842767,求直线n的斜率.
单选题 | 一般(0.65) | 2021·全国高二课时练习
解题方法
同步
3 . 已知抛物线eqId2381423d4cd146cab95f55527681a766的顶点在原点,焦点在eqId072d7d6b911b42bc89207e72515ebf5f轴正半轴上,过其焦点eqId63db14a5b4334f3ea583c8fb12b0d175作直线eqId417e80f1349244878d01fe90e0891f5f交抛物线于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,过点eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c分别作抛物线准线的垂线,垂足分别为点eqId19a4eb16029e4550a14f2afe4741a3c3eqId312ef2c826304089b9b0f1d1e88b0f50eqIdf00baa3c19ea406988930c25801b233e,且eqId0505f300492746ba8eef675f6ba79d44,则该抛物线的方程为(   )
A.eqIddcd4380c728f43a495cce5036f34b97dB.eqId89d878a570404f8a96f2de5cfa3a0f08C.eqId492a7a8eda394265bac7139cc1a683abD.eqIda4a476376a064674870547e7f624c4a6
解答题 | 一般(0.65) | 2021·河北张家口·高二期末
解题方法
4 . 已知抛物线eqId91d153665f12451bb66d663cf54c2b6a经过点eqId854ffce3f6ef441c9e79cce15c0632e0
(1)求抛物线C的标准方程;
(2)经过点eqId998a5d5a212c46efa96c585d6ac13318的直线l与抛物线C相切于点B(点B在第一象限),O是坐标原点,圆O与直线l相切于点E,设eqId00a644589e654b3e9dccf44fb07c5291,求实数λ的值.
解答题 | 一般(0.65) | 2020·山东高考真题
解题方法
5 . 已知抛物线的顶点在坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b,椭圆eqId69b431a08ada48629fa1b026adc90e0c的顶点分别为eqId346946f1395a41008d3b3b56c9ae4fbdeqId894f8d53415741dea8f7a841c68384d1eqIde660daa143d5431e96530c61b610d572eqId01ad4ec8cf0543da939adaa52264b614,其中点eqId894f8d53415741dea8f7a841c68384d1为抛物线的焦点,如图所示.
说明: figure
(1)求抛物线的标准方程;
(2)若过点eqId346946f1395a41008d3b3b56c9ae4fbd的直线eqId417e80f1349244878d01fe90e0891f5f与抛物线交于eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6两点,且eqId32518421280b4d0e86555b9f561f32f4,求直线eqId417e80f1349244878d01fe90e0891f5f的方程.
填空题 | 一般(0.65) | 2020·河北正定中学
解题方法
典型
6 . 已知点eqId7a121e09cf94401a96a62c05680df30b在抛物线eqId93cbffaa5ae045d6ac45d1e979991c3aeqIdf91aad2290ad408799ceac6f8a03ae91上,过点eqId25e81b8bd3424e438ace3b13a1b3b419的直线eqId417e80f1349244878d01fe90e0891f5f交抛物线eqId93cbffaa5ae045d6ac45d1e979991c3aeqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,若eqId92f3f60dafe749178a8bfef1e2d39843,则直线eqId417e80f1349244878d01fe90e0891f5f的倾斜角为________
7 . 直线eqIdd0fe55aca76741539b1a6f53e363a19ceqIda9cd3f94eb8045438f75e9daccfa7200轴于点eqIdbedf755e0fdb4d078d6859360706b163,交椭圆上eqIdd448b721bc2f41f8bed63e9521739ce3eqId207ddd75d0ee42629ce30bec7dcdaba1)于相异两点eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c,且eqIdc5ce041359014968bdb38afcbed60d27
(1)求eqId70a27b6ddf6b478285353abb3b1f3741的取值范围;
(2)将弦eqId99a3187c2b8f4bcc9703c74c3b72f1f3绕点eqId052844cae8574a8ab842c38a039baac0旋转eqId194b4d8e42254eaeaab1535e05205ed9得到线段eqId0c43edec1bef4ede93a413694f6f5d55,设点eqId75a143b898e14ccdb032561fba9da811的坐标为eqIda990bec8b31d4a66a8d9231a9341c1dd,求证:eqIdbc1e289ee992494a9706aba07312d9ea
8 . 已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的中心为坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b,一个长轴端点为eqIdd2d791f456914a80af33c93c5cc6ea11,短轴端点和焦点所组成的四边形为正方形,直线eqId417e80f1349244878d01fe90e0891f5feqId072d7d6b911b42bc89207e72515ebf5f轴交于点eqId9cda99dba8d74312be9e06ed7f7299fc,与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3交于相异两点eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c,且eqIdc5c2b94f473b4b85a6ecaac012f910ce
(1)求椭圆的方程;
(2)求直线eqId417e80f1349244878d01fe90e0891f5f的方程.
解答题 | 一般(0.65) | 2021·上海市长征中学高二期中
解题方法
9 . 点eqId753b2bb5c9bf4a0f90e545946f74595a是双曲线EeqId0f14428848fa4e8cbdaccdcb9711090d上一点,MN分别是双曲线E的左、右顶点,直线PMPN的斜率之积为eqIde1490df2d2c84688942d45fd01c90a85
(1)求eqId84bb3bf2bcd4450c85dd7570191c36fc的值;
(2)过双曲线E的右焦点且斜率为1的直线交双曲线于AB两点,O为坐标原点,C为双曲线上的一点,满足eqId994b4e034592442a8105bd6b639c9be6,求eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c的值.
解答题 | 一般(0.65) | 2021·宁波市北仑中学高三开学考试
解题方法
压轴
10 . 如图,已知eqId03032eef35c64c23b0901ccd08612ae8,直线eqId499de1fe82034616a18069816e30263deqIdbedf755e0fdb4d078d6859360706b163是平面上的动点,过点Pl的垂线,垂足为点Q,且eqIddc730b4e7efb47caa1e840996c7e1a68
说明: figure
(1)求动点P的轨迹C的方程;
(2)过点F的直线交轨迹CAB两点,交直线l于点M
①已知eqIda14962acc4814b25a4a5d55d0e50bc95,求eqId5fcc095f479e49a6a3da0514b84908b5的值;
②求eqId0d99f23fa2db4a3a99e7bd45dfe0ad9c的最小值.