组卷网>知识点选题>利用参数方程解决范围或最值问题
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1 . 已知曲线eqId19a4eb16029e4550a14f2afe4741a3c3的极坐标方程为eqId33312e4be2b94a8aaaf364666aabdd26,点eqIdd65805361da5481bb7670e89555e89d3eqId73bd354ad8c44353a051ca4895390edbeqIdc61af9056e4148fd9287cf000b2c721a都在曲线eqId19a4eb16029e4550a14f2afe4741a3c3上.
(1)当eqId2a9c6904e3f34d91b7da3ca06c06c05e时,求直线eqId10381e9fca8b4095b66c934255c907b4的极坐标方程;
(2)以极点eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,极轴为eqIda9cd3f94eb8045438f75e9daccfa7200轴的正半轴,建立平面直角坐标系.当eqId2381423d4cd146cab95f55527681a766eqId19a4eb16029e4550a14f2afe4741a3c3上运动时,求eqId7f2462dce9654597939aaa12d29d62b4的取值范围.
2 . 已知椭圆eqId680a224f4d4045c1925d9f7ae696464a与直线eqId0da35a4003144bf58cc68e26d0b3f798
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的参数方程与直线eqId417e80f1349244878d01fe90e0891f5f的极坐标方程;
(2)在椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上求一点eqId2381423d4cd146cab95f55527681a766,使得点eqId2381423d4cd146cab95f55527681a766到直线eqId417e80f1349244878d01fe90e0891f5f的距离最小,并求出最小距离.
3 . 在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,直线eqId417e80f1349244878d01fe90e0891f5f的方程为eqIde346783907434485a70c4254255f5ed0,以原点为极点,以eqIda9cd3f94eb8045438f75e9daccfa7200轴正半轴为极轴建立极坐标系,圆eqId19a4eb16029e4550a14f2afe4741a3c3的极坐标方程为eqIdbb7b87fec393443bac46fe4693716651.
(1)求圆eqId19a4eb16029e4550a14f2afe4741a3c3的直角坐标方程和直线eqId417e80f1349244878d01fe90e0891f5f的极坐标方程;
(2)求圆eqId19a4eb16029e4550a14f2afe4741a3c3上的点到直线eqId417e80f1349244878d01fe90e0891f5f的最短距离.
4 . 已知直线eqId5ff0e2e4422945e0bf3006fb112db7bf为参数,eqIdb9adb1c1dcd3471ea157536fed5d455e)经过椭圆eqId4573a9a3fe9c446c848e7ded939d36b8为参数)的左焦点eqId63db14a5b4334f3ea583c8fb12b0d175
(1)求eqIda4be99d332154d13a4a6ed1ff6444fe7的值;
(2)设直线eqId417e80f1349244878d01fe90e0891f5f与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdeb53cb7cb0274f7d8f111c60f824c243两点,求eqIdc08e1cdc467b488aa066d90d8cbaebb9的最小值.
(3)设eqId80035461defb4251b7c86f4e8c74f3e7的三个顶点在椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上,求证,当eqId2efda802d5534f6d92d9f8af7aaec28beqId80035461defb4251b7c86f4e8c74f3e7的重心时,eqId80035461defb4251b7c86f4e8c74f3e7的面积是定值.
5 . 在极坐标系中,直线l的极坐标方程为eqIdb3084d52db8c4a1c94bf61308bd36477,以极点为坐标原点,极轴为x轴的正半轴建立平面直角坐标系,曲线C的参数方程为eqId996e4585224645dbb5bc044ce2a578e5t为参数),点A是曲线C上的动点.
(Ⅰ)求直线l的直角坐标方程;
(Ⅱ)求点A到直线l的距离的最小值.
6 . 已知:椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId80b0de2612e546db8b9e7d6f69578960,直线eqId417e80f1349244878d01fe90e0891f5feqIdc9b69cf7b1fe4968bbf692081453d229,求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上一点eqIdbedf755e0fdb4d078d6859360706b163到直线eqId417e80f1349244878d01fe90e0891f5f的距离的最小值__________.
7 . 已知曲线C1eqIddf4f7cbde050447da0688833c2524258t为参数),C2eqIdd38ce036e5104570904abcd6fe561e10α为参数且eqId0ecb20a47e9d4970a8c48ac761f05b33),在以原点O为极点,x轴非负半轴为极轴的极坐标系中,直线C3θeqId9e7f9209cee04cdb9a06395310730b31ρR).
(1)求曲线C1C2的普通方程;
(2)若C2上的点P对应的参数αeqId2cb51764ae3949b9b698fc2f9527dff2QC1上的点,求PQ的中点M到直线C3距离d的最小值.
解答题 | 一般(0.65) | 2021·山西(文)
8 . 在直角坐标系xOy中,曲线C的参数方程为eqId15347d96c46f47ae9fb13dbe8288378beqIdc13953f2514e4c8f9c8aaaf5241c33ac为参数).以坐标原点为极点,x轴正半轴为极轴建立极坐标系,直线l的极坐标方程为eqId5655a339f7d94c96b80687d05a4722bf
(1)分别求出C的普通方程和l的直角坐标方程;
(2)设点PC上,点Ql上,求eqIdb30a7f74215a45849f88704ca844a445的最小值.
9 . 在直角坐标系eqId2272a344734c4fb088737b84294f7219中,曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的参数方程为eqId199fc3a9186a4ab586c7b128b8bf0e3eeqId69f56ef2c88b4b73a560da59f5247a82为参数).以坐标原点为极点,eqIda9cd3f94eb8045438f75e9daccfa7200轴正半轴为极轴建立极坐标系,曲线eqId3a63d00111554b9e8b896929779a293d的极坐标方程为eqId936e003e0bff4221af78e797ce5ca339.
(1)求曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的普通方程和eqId3a63d00111554b9e8b896929779a293d的直角坐标方程;
(2)设曲线eqIdcfc8599bedfb4ab4944abf141f348a9aeqId3a63d00111554b9e8b896929779a293d交于不同的eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,求eqId4819509fefec4542acccfcf3d67cd699.
10 . 在极坐标系中,曲线eqId19a4eb16029e4550a14f2afe4741a3c3的方程为eqId54ac7e960c6f40eabd6cb60796be13cb,以极点为直角坐标系的原点,极轴为eqIda9cd3f94eb8045438f75e9daccfa7200轴正半轴建立直角坐标系eqId5231dd4389ce4a51959d8d4b3e4b9923
(1)求曲线eqId19a4eb16029e4550a14f2afe4741a3c3的直角坐标方程,并说明eqId19a4eb16029e4550a14f2afe4741a3c3是什么曲线;
(2)直线eqId417e80f1349244878d01fe90e0891f5f的参数方程为eqIda59751686f28471ba55daa47bd27b106为参数,eqId2e89aaf57b06426a9c9d7e2fd8a15e9c,点eqIdbedf755e0fdb4d078d6859360706b163的直角坐标为eqId368e044eb8b14b19b5725a4022161087,直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdeb53cb7cb0274f7d8f111c60f824c243两点,求eqId2906f63998244f46b91b3f3721fc22e7的最大值.
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