组卷网>高中数学综合库>坐标系与参数方程>曲线的参数方程>参数方程与普通方程的互化>参数方程化为普通方程
题型:解答题 难度:0.65 引用次数:992 更新时间:2020/11/27 8:36:48 题号:11826359
在平面直角坐标系eqId10574e871de54180ba4f99615dc829f7中,直线eqId417e80f1349244878d01fe90e0891f5f的参数方程为eqIdb4d5dff851a04b7e9a757987fe20cbcbeqId69f56ef2c88b4b73a560da59f5247a82为参数).以eqId762907fcf5384cbfa90b8f905ac41675为极点,eqId554db84bf95a4faeb5c586bd4e245241轴的正半轴为极轴,建立极坐标系,曲线eqIdbc41f56700514788b80ac5f332b3baf6的极坐标方程为eqId4a5ad78f0339405c85dcfaaccda24f7d,且曲线eqIdbc41f56700514788b80ac5f332b3baf6与直线eqId417e80f1349244878d01fe90e0891f5f有且仅有一个公共点.
(1)求eqId70a27b6ddf6b478285353abb3b1f3741
(2)设eqIdeb53cb7cb0274f7d8f111c60f824c243曲线eqIdbc41f56700514788b80ac5f332b3baf6上的两点,且eqId807f07cf3346459888342a16e939fd07,求eqIdb5886138924a4a5a847a52fac766656e的最大值.

类题推荐

解答题 | 一般(0.65) |
【推荐1】在直角坐标系eqId94e28bb883384a7580bda6b481c94427中,已知曲线eqIdcfc8599bedfb4ab4944abf141f348a9aeqId3a63d00111554b9e8b896929779a293d的参数方程分别为eqIdcfc8599bedfb4ab4944abf141f348a9aeqId559f84f4d725413c8ed54d4d07a465a3eqId6143f9bfc1f34069adacbcbc6f4c3e4ceqId3a63d00111554b9e8b896929779a293deqIdd85e5bde9d6a4af9b5f474326c1fd679eqIdb2c21f1b82214d5387a7afa3bf0424ef.
(1)求曲线eqIdcfc8599bedfb4ab4944abf141f348a9aeqId3a63d00111554b9e8b896929779a293d的普通方程;
(2)已知点eqIde54a6f7ae55b4e95bbb91f5217d72a90,若曲线eqIdcfc8599bedfb4ab4944abf141f348a9a与曲线eqId3a63d00111554b9e8b896929779a293d交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,求eqIda9243019b38c423dbaab882bf708e088的取值范围.
更新:2018/11/26组卷:2269
解答题 | 一般(0.65) |
【推荐2】选修4-4:坐标系与参数方程
在直角坐标系eqId2272a344734c4fb088737b84294f7219中,曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的普通方程为eqId9633ed124b9443bab46dab59547856a9,曲线eqIdfe33ac7524b14f658e64c52c37499d5c的参数方程为eqId1c1a2f3c28ab43a7b72de88c07e07ab8eqIdf9db0aee08264a238b9741675591065e为参数),以坐标原点为极点,eqIdc12aac8c2448479687a40735b3572a23轴正半轴为极轴建立极坐标系,直线eqId417e80f1349244878d01fe90e0891f5f的极坐标方程为eqIdb3f5e715ed81425198b2544c9a7f2e7f.
(1)求曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的极坐标方程和曲线eqIdfe33ac7524b14f658e64c52c37499d5c的普通方程;
(2)直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqIdcfc8599bedfb4ab4944abf141f348a9a在第一象限内的交点为eqIdd7be5abad1e34f6db17a56660de8d54f,过点eqIdd7be5abad1e34f6db17a56660de8d54f的直线eqIda20558bac276438caa0c85b6224a1e5c交曲线eqIdfe33ac7524b14f658e64c52c37499d5ceqIdeb53cb7cb0274f7d8f111c60f824c243两点,且eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点为eqIdd7be5abad1e34f6db17a56660de8d54f,求直线eqIda20558bac276438caa0c85b6224a1e5c的斜率.
更新:2019/02/23组卷:571
解答题 | 一般(0.65) |
【推荐3】选修4-4:坐标系与参数方程
已知在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,曲线eqId19a4eb16029e4550a14f2afe4741a3c3的参数方程为eqIdf0261dc56ccb4f70a64a2fe3a173bc5beqId50619b805a9743fe980db51e08985a46为参数)
(1)求曲线eqId19a4eb16029e4550a14f2afe4741a3c3的普通方程;
(2)经过点eqId27c65abd6f7b4e0dbb2afd75e5513413(平面直角坐标系eqId2272a344734c4fb088737b84294f7219中的点)作直线eqId417e80f1349244878d01fe90e0891f5f交曲线eqId19a4eb16029e4550a14f2afe4741a3c3eqIdeb53cb7cb0274f7d8f111c60f824c243两点.若eqIdbedf755e0fdb4d078d6859360706b163恰好为线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3中点,求直线eqId417e80f1349244878d01fe90e0891f5f的方程.
更新:2020/10/18组卷:692
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