组卷网>知识点选题>直线的参数方程中参数的几何意义解决距离问题
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1 . 已知经过点eqId29080c91a1b44f30aa5d9bc21982c0f4的直线eqId417e80f1349244878d01fe90e0891f5f的倾斜角为eqId9e7f9209cee04cdb9a06395310730b31,曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的参数方程为eqIdbc9960ae338340968752b8a14f9b33edeqId6c9518e43fd5459798a30cfc10026e3c为参数),直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqIdcfc8599bedfb4ab4944abf141f348a9a交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点.
(1)求曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的普通方程及直线eqId417e80f1349244878d01fe90e0891f5f的参数方程;
(2)求eqId51f1ba44123f4fa9b3b071efe519e6b7的值.
2 . 在直角坐标系eqId2272a344734c4fb088737b84294f7219中,直线eqIdcfc8599bedfb4ab4944abf141f348a9a的参数方程为eqId16b3ac5ca5754c86b9fb038bc50a0561(其中eqId69f56ef2c88b4b73a560da59f5247a82为参数).以坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b为极点,eqIda9cd3f94eb8045438f75e9daccfa7200轴非负半轴为极轴建立极坐标系,曲线eqId3a63d00111554b9e8b896929779a293d的极坐标方程为eqId2518c3e929b749af902fd77ff6e2094b
(1)求eqIdcfc8599bedfb4ab4944abf141f348a9aeqId3a63d00111554b9e8b896929779a293d的直角坐标方程;
(2)设定点eqId36549e9eac35406780cb4574095b3ff0,直线eqIdcfc8599bedfb4ab4944abf141f348a9a交曲线eqId3a63d00111554b9e8b896929779a293deqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,求eqId85137889b7ce42fab4cd6e31bb8feabe的值.
3 . 已知曲线eqIdcfc8599bedfb4ab4944abf141f348a9aeqId758e25060e8d40e0852fd1ee236716a4eqId69f56ef2c88b4b73a560da59f5247a82为参数),曲线eqId3a63d00111554b9e8b896929779a293deqId35d223ade1954f1981be9deecdb6d950
(1)求eqIdcfc8599bedfb4ab4944abf141f348a9a的普通方程与eqId3a63d00111554b9e8b896929779a293d的直角坐标方程;
(2)若曲线eqIdcfc8599bedfb4ab4944abf141f348a9a与曲线eqId3a63d00111554b9e8b896929779a293d交于eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6两点,交eqIda9cd3f94eb8045438f75e9daccfa7200轴于点eqIdbedf755e0fdb4d078d6859360706b163,求eqIdf6f0c520999d499cb568474c6469ca0e的值.
4 . 在直角坐标系eqId2272a344734c4fb088737b84294f7219中,直线eqId417e80f1349244878d01fe90e0891f5f的参数方程为eqId84fa6e0112bc4400a2d498107f44be57(eqId69f56ef2c88b4b73a560da59f5247a82为参数),以坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b为极点,eqIda9cd3f94eb8045438f75e9daccfa7200轴的正半轴为极轴建立极坐标系,曲线eqId19a4eb16029e4550a14f2afe4741a3c3的极坐标方程为eqId1f59f1b713f64a0f8e064763dad90964.
(1)求直线eqId417e80f1349244878d01fe90e0891f5f的普通方程和曲线eqId19a4eb16029e4550a14f2afe4741a3c3的直角坐标方程;
(2)若直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqId19a4eb16029e4550a14f2afe4741a3c3交于eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6两点,设eqId7063803412cd4003948673a35fd10874,求eqIdf6f0c520999d499cb568474c6469ca0e的值.
5 . 在直角坐标系eqId2272a344734c4fb088737b84294f7219中,曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的参数方程为eqIdd384b12ad2f8425295495ba1100df1eft为参数),以原点为极点,x轴的正半轴为极轴建立极坐标系,曲线eqId3a63d00111554b9e8b896929779a293d的极坐标方程为eqIdb3b0e15b548749e1a44728a6bd2adbe9
(1)求曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的普通方程和曲线eqId3a63d00111554b9e8b896929779a293d的直角坐标方程;
(2)若P的直角坐标为eqIdafed4da885124e6a9b4b7e8d5053b1e3,曲线eqId3a63d00111554b9e8b896929779a293d与曲线eqIdcfc8599bedfb4ab4944abf141f348a9a交于AB两点,求eqId52afd667d68143f0bc9493b8f64c358b的值.
6 . 已知在极坐标系中,点A的极坐标为eqId4efa3f3de8cf40b4acc90c6b93363fff,曲线eqId96240d600bba4d3d94260a5ebe120fc2.以极点为坐标原点,极轴为x轴正半轴,建立直角坐标系,若直线lA点,且倾斜角为eqId6c9518e43fd5459798a30cfc10026e3c
(1)求直线l的参数方程与曲线C的直角坐标方程;
(2)若直线l与曲线C交于BC两点,且eqIdbab5de418ecd4881b2c20b0b7b2c864a,求直线l的斜率.
7 . 坐标系与参数方程已知圆C的极坐标方程为eqId5786e1358a00447ca30aa6b1c158fd6b,直线eqId417e80f1349244878d01fe90e0891f5f的参数方程为eqIdc4a91e6106574aad88fe8a26525ea4a6eqId69f56ef2c88b4b73a560da59f5247a82为参数).
(1)把圆eqId19a4eb16029e4550a14f2afe4741a3c3的极坐标方程化为直角坐标方程;
(2)求直线eqId417e80f1349244878d01fe90e0891f5f被圆eqId19a4eb16029e4550a14f2afe4741a3c3截得的线段AB的长.
8 . 已知直线eqId417e80f1349244878d01fe90e0891f5f经过点eqId3c88cf2dc0e84356adb99d553a9a9f08,倾斜角eqId738fdab180ef4987b09579a26fc4074a,圆C的极坐标方程为eqId7b24f3417e6646c68edaa448a9fc8629.
(1)写出直线eqId417e80f1349244878d01fe90e0891f5f的参数方程,并把圆eqId56c9c70b2f4b4c789a22f1b2aa3d29aa的极坐标方程化为直角坐标下的普通方程;
(2)设eqId417e80f1349244878d01fe90e0891f5f与圆eqId19a4eb16029e4550a14f2afe4741a3c3相交于eqIdeb53cb7cb0274f7d8f111c60f824c243两点,求点eqIdbedf755e0fdb4d078d6859360706b163eqIdeb53cb7cb0274f7d8f111c60f824c243两点的距离之积eqId9120ba0071d543faa9de28707205bc6d
9 . 在极坐标系中,曲线eqIdbecfc61990da415dbbc39f953b1e01f5,以极点为坐标原点,极轴为轴正半轴建立直角坐标系eqId2272a344734c4fb088737b84294f7219,曲线eqId3a63d00111554b9e8b896929779a293d的参数方程为eqId30398e23ee2d46789ab0716feb3e0a08eqId69f56ef2c88b4b73a560da59f5247a82为参数).
(1)求eqIdcfc8599bedfb4ab4944abf141f348a9a的直角坐标方程与eqId3a63d00111554b9e8b896929779a293d的普通方程;
(2)若曲线eqIdcfc8599bedfb4ab4944abf141f348a9a与曲线eqId3a63d00111554b9e8b896929779a293d交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,且定点eqIdbedf755e0fdb4d078d6859360706b163的坐标为eqIdafed4da885124e6a9b4b7e8d5053b1e3,求eqId23dc25b0d2fd425da88aaf6ff3e43703的值.
10 . 在平面直角坐标系中,曲线C的参数方程为eqId4539f767067140c0a70d203694826193eqId145940d03af4447eabd753d76abd2a1d为参数),直线l的参数方程为eqId16a40e1fcd8d46f298044d504ea74851eqId69f56ef2c88b4b73a560da59f5247a82为参数),以坐标原点为极点,x轴的正半轴为极轴建立极坐标系.
(1)求曲线C的极坐标方程以及直线l的普通方程;
(2)若eqId3deaf6d16cf84f17a60709d6c1f8f277,直线l与曲线C相交于不同的两点MN,求eqId57297da7b41043778ae074b5196d6d8b的值.
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