组卷网>知识点选题>几何法求弦长
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1 . 已知直线eqIdcb408cdb9cd04b05bef100061f2c1430t为参数),曲线eqIdf691fdb4529a438aa01bf89b3da55acc
(1)求直线eqIdcfc8599bedfb4ab4944abf141f348a9a的普通方程与曲线eqId3a63d00111554b9e8b896929779a293d的直角坐标方程;
(2)求直线eqIdcfc8599bedfb4ab4944abf141f348a9a被曲线eqId3a63d00111554b9e8b896929779a293d所截得的弦长.
单选题 | 较易(0.85) | 2021·广西河池市·高二期末(文)
解题方法
2 . 已知斜率为eqIdbeffaaf8d5cd43cf8375210d69fce6be的直线eqId417e80f1349244878d01fe90e0891f5f被圆eqId19a4eb16029e4550a14f2afe4741a3c3eqIdae3d4095f09d454c9a104d423e4e4a92截得的弦长为eqId807b61b62f09462994e31cf497210538,则直线eqId417e80f1349244878d01fe90e0891f5f的方程为(   )
A.eqId7ef234275e784efaae5217eccc9a7f0eeqIdbd2c8e6823a44ae5af525275c4523ccf
B.eqId1642e65278b14670b8d166488392b92feqId41af6300a6614fe3beee0146eb3c7e96
C.eqId10377b4dea7042b48d34dfb46c9beab6eqIde5fcb1d98dab480e9ef83a2e7ceaa0b4
D.eqIda14da2618dc04897956ab9abc800a93ceqId14a346e8d395488aad2bc51987f8fbad
3 . (1)求经过点eqId82537fdd3eea4572b1ce70941de33977,点eqId55d2276dc69a457babd491d85ad87a04,且圆心在直线eqId762500ba8ef1409c9131f0f2fd5091ac上的圆的方程;
(2)已知圆eqId19a4eb16029e4550a14f2afe4741a3c3上的点eqId366040149ff640f385d54b009a9c6f29关于直线eqId177c047ef4a54a738707545fff93dae8的对称点仍在圆eqId19a4eb16029e4550a14f2afe4741a3c3上,圆eqId19a4eb16029e4550a14f2afe4741a3c3的面积为eqIda0aba3c9a8dd4a4cac52ba27bcd80753,圆心eqId19a4eb16029e4550a14f2afe4741a3c3在第二象限,且直线eqId312e64547fa244caafa4bb8b9fe657bb与圆eqId19a4eb16029e4550a14f2afe4741a3c3相交于eqId93cbffaa5ae045d6ac45d1e979991c3aeqId63db14a5b4334f3ea583c8fb12b0d175两点,求eqIdbab9b685a75b4fea966282b699e18edf
填空题 | 较易(0.85) | 2021·云南保山市·高二期末(理)
解题方法
4 . 已知双曲线的标准方程为eqId7c48d518d78b4835b0ab560aadc005f2,其右焦点为eqId0aa72756ed0c4c7a89f26aa94f43e47d,以eqIdb49e5250cb494bff964531f3bb12d2f0为直径的圆和直线eqIda9d8558290c64896b00f1c4577d0d92f相交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,则eqId767a74dd06384d9d903c87d6375db07e_____
解答题 | 较易(0.85) | 2021·贵州贵阳市·高一期末
解题方法
5 . 已知以点eqIdbe973624835548d9b3b266400250beba为圆心的圆与直线eqId36ba90a9b96a4ead95bcf58d71d2ba42相切,过点eqIdc8bccf4a759e468b91cd934877956fcd的动直线eqId417e80f1349244878d01fe90e0891f5f与圆eqId052844cae8574a8ab842c38a039baac0相交于eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6两点.
(1)求圆eqId052844cae8574a8ab842c38a039baac0的方程;
(2)当eqIdcce1007c64124b719b74a467092c3ccf时,求直线eqId417e80f1349244878d01fe90e0891f5f的方程.
单选题 | 一般(0.65) | 2021·河南开封市·高二期末(文)
解题方法
6 . 已知直线eqId417e80f1349244878d01fe90e0891f5f经过点eqId769253c23014435e8a96b6bd66657930,且点eqId6f59345efc7948c1972984d90bf41ac5eqIdcd41fd5b7a704b179bf50c0dc7130d8beqId417e80f1349244878d01fe90e0891f5f的距离相等,则eqId417e80f1349244878d01fe90e0891f5f被经过eqId2efda802d5534f6d92d9f8af7aaec28beqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c三点的圆所截得的弦长为(   )
A.eqId53671357a7b04686a6a8915d8fb778d4eqId5d04f8a500ff47769300856360b7f29aB.eqId801221b85ed147bba6ce222ebce7d57eC.eqId801221b85ed147bba6ce222ebce7d57eeqId5d04f8a500ff47769300856360b7f29aD.eqId5d04f8a500ff47769300856360b7f29a
解答题 | 一般(0.65) | 2021·全国高一专题练习
解题方法
7 . 已知圆eqId69c89622f24b47f9bc9e12f3d1bef7fc.问是否存在斜率为1的直线l,使l被圆C截得的弦eqId99a3187c2b8f4bcc9703c74c3b72f1f3满足:以eqId99a3187c2b8f4bcc9703c74c3b72f1f3为直径的圆经过原点?
8 . 已知圆eqId19a4eb16029e4550a14f2afe4741a3c3eqIdae3d4095f09d454c9a104d423e4e4a92
(1)若直线eqId417e80f1349244878d01fe90e0891f5f过点eqId68ecd802e7c84202bb9404e62b23b157且被圆eqId19a4eb16029e4550a14f2afe4741a3c3截得的弦长为eqIdc052ddfbd4524f67a79e0e77c2e5656a,求直线eqId417e80f1349244878d01fe90e0891f5f的方程;
(2)从圆eqId19a4eb16029e4550a14f2afe4741a3c3外一点eqIdbedf755e0fdb4d078d6859360706b163向圆eqId19a4eb16029e4550a14f2afe4741a3c3引一条切线,切点为eqId2381423d4cd146cab95f55527681a766eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,且eqIdf004bbadc075453e8b5d14e6e7cfd92e,求eqId4eeb399976fc4d00a5d54aaf750ff661的最小值.
填空题 | 容易(0.94) | 2020·天津高三二模
解题方法
9 . 过原点且倾斜角为eqIdf1c3337151994ec4b99354c9d54f311c的直线与圆eqId3dfecd6b24bb4825a9537ae81f6e59cf相交,则直线被圆截得的弦长为_____.
单选题 | 容易(0.94) | 2021·贵州贵阳一中高三月考(文)
解题方法
10 . 圆CeqIdfb8c7050e7bc4c5f98aeb191f3f5b673被直线eqId6ca11d2504114831afc2e03724b3b2e0截得的最短弦长为(   )
A.eqId7bcd573cee334383ad72cc4b179fcfb3B.eqId2644c4fd7d684e75ae5ed93cb3581244C.eqIda2a0ce3781fa4c26b624f5966b7dee44D.eqId317ed84d205b4156847380f7e9f38b08
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