组卷网>知识点选题>弦长问题
显示答案
| 共计 270 道试题
1 . 在平面直角坐标系中,圆C的参数方程为eqId61238a7ec85a4f7aa0ff846c980bd858α为参数),以坐标原点为极点,以x轴的正半轴为极轴建立极坐标系,且长度单位相同.
(1)求圆C的极坐标方程;
(2)若过原点的直线l被圆C截得的弦长为2,求直线l的倾斜角.
填空题 | 一般(0.65) | 2021·河南洛阳市·高二期末(文)
解题方法
2 . 在极坐标系中,直线eqId49677cbbe8474d148bd40ba918500842和圆eqId2edfbf94c73042d698a85eb5704a4a15交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,则eqId767a74dd06384d9d903c87d6375db07e______.
3 . 在直角坐标系eqId2272a344734c4fb088737b84294f7219中,曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的参数方程为eqId9e28ea49c2cb43a1a484daa9d54b8872(eqIdc13953f2514e4c8f9c8aaaf5241c33ac为参数),以坐标原点为极点,eqIda9cd3f94eb8045438f75e9daccfa7200轴的正半轴为极轴建立极坐标系,曲线eqId3a63d00111554b9e8b896929779a293d的方程为eqIdb5229bf0210e4a6b9ef098d4908c27be.
(1)求eqIdcfc8599bedfb4ab4944abf141f348a9aeqId3a63d00111554b9e8b896929779a293d交点的直角坐标;
(2)过原点eqId2efda802d5534f6d92d9f8af7aaec28b作直线eqId417e80f1349244878d01fe90e0891f5f,使eqId417e80f1349244878d01fe90e0891f5feqIdcfc8599bedfb4ab4944abf141f348a9aeqId3a63d00111554b9e8b896929779a293d分别相交于点eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c(eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c与点eqId2efda802d5534f6d92d9f8af7aaec28b均不重合),求eqId4819509fefec4542acccfcf3d67cd699的最大值.
4 . 在直角坐标系eqId2272a344734c4fb088737b84294f7219中,已知曲线eqId19a4eb16029e4550a14f2afe4741a3c3的参数方程是eqId3e9453148461428c9b247e933dc780d3eqId69f56ef2c88b4b73a560da59f5247a82为参数),若以原点为极点,以eqIda9cd3f94eb8045438f75e9daccfa7200轴正半轴为极轴建立极坐标系,曲线eqId0cd8063abf2b458f80091bc51b75a904的极坐标方程是eqIdce9fdbb66bf14aeeaf34fedafe4b0f74
(1)求曲线eqId19a4eb16029e4550a14f2afe4741a3c3的普通方程和曲线eqId0cd8063abf2b458f80091bc51b75a904的直角坐标方程;
(2)若射线eqId417e80f1349244878d01fe90e0891f5feqIdb42bc0ae85294d1f9e6800ac7c568097eqIdac0194101a6e428d894b06594a73568d与曲线eqId19a4eb16029e4550a14f2afe4741a3c3和曲线eqId0cd8063abf2b458f80091bc51b75a904分别交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,求eqId4819509fefec4542acccfcf3d67cd699
解答题 | 一般(0.65) | 2021·全国高二专题练习(文)
5 . 在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,曲线eqId19a4eb16029e4550a14f2afe4741a3c3的参数方程为eqIdbfb0f2e880cb45d69a506d9cbc944433eqIdc13953f2514e4c8f9c8aaaf5241c33ac为参数),以eqId2efda802d5534f6d92d9f8af7aaec28b为极点,以eqIda9cd3f94eb8045438f75e9daccfa7200轴的非负半轴为极轴的极坐标系中,直线eqId417e80f1349244878d01fe90e0891f5f的极坐标方程为eqId0a8cae9c33cd4f82bf47b6180fa29ccb.
(1)求曲线eqId19a4eb16029e4550a14f2afe4741a3c3的极坐标方程;
(2)设直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqId19a4eb16029e4550a14f2afe4741a3c3相交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,求eqId4819509fefec4542acccfcf3d67cd699的值.
6 . 已知圆eqIdd50cb90343894f8fae640dcadf643885的圆心为eqIdff343dc03adf4062b1306213897b270e,半径为eqIdcd9b24a6a6e5426ab775be20461174e3,在以原点eqId2efda802d5534f6d92d9f8af7aaec28b为极点,eqIda9cd3f94eb8045438f75e9daccfa7200轴正半轴为极轴的极坐标系中,圆eqIdb12a09e77857490c848c79bcf0414e8f的方程为eqId065a789817ea4351b36eaa2337bcbef3
(1)求圆eqIdd50cb90343894f8fae640dcadf643885的极坐标方程;
(2)若圆eqIdd50cb90343894f8fae640dcadf643885与圆eqIdb12a09e77857490c848c79bcf0414e8f的公共弦长为eqId09e05062a16b4f488a1f9b4f661d0c75,求圆eqIdb12a09e77857490c848c79bcf0414e8f的极坐标方程.
7 . 在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,以坐标原点为极点,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eqId45841002f078405da759c3d9a9d8c680
(1)求曲线eqId19a4eb16029e4550a14f2afe4741a3c3与极轴所在直线围成图形的面积;
(2)设曲线eqId19a4eb16029e4550a14f2afe4741a3c3与曲线eqId14f402d5ad994f8da9a443345dd0eb3b交于eqIdeb53cb7cb0274f7d8f111c60f824c243两点,求eqId4819509fefec4542acccfcf3d67cd699
8 . 在平面直角坐标系中,曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的参数方程为eqId2b0bb2ae7d7c46f4b5bb5d4e03415665eqIdc13953f2514e4c8f9c8aaaf5241c33ac为参数).以坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b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eqId9b258780dcb64e9680cf5f715d8ad655.
(Ⅰ)求曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的极坐标方程和曲线eqId3a63d00111554b9e8b896929779a293d的直角坐标方程;
(Ⅱ)已知直线eqId417e80f1349244878d01fe90e0891f5f的极坐标方程为eqId796620a035dd46c1a58638246201352ceqId417e80f1349244878d01fe90e0891f5f分别与曲线eqIdcfc8599bedfb4ab4944abf141f348a9aeqId3a63d00111554b9e8b896929779a293d交于点eqId052844cae8574a8ab842c38a039baac0(异于点eqId2efda802d5534f6d92d9f8af7aaec28b)和点eqId8754ce8cf7f34f04abb9a0c041f57f5c,求线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3的长.
9 . 在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,已知射线eqId8fad5ca5a9db4058af85707778b3094d,曲线eqIdfb3ea9c985ad4bccb1c4eb083a322f94eqId69f56ef2c88b4b73a560da59f5247a82为参数).以原点eqId2efda802d5534f6d92d9f8af7aaec28b为极点,eqIda9cd3f94eb8045438f75e9daccfa7200轴的非负半轴为极轴建立极坐标系,曲线eqId3a63d00111554b9e8b896929779a293d的极坐标方程为eqId6cf509a187d341838d67eca87cbc0d9b.
(1)写出射线eqId417e80f1349244878d01fe90e0891f5f的极坐标方程以及曲线eqIdcfc8599bedfb4ab4944abf141f348a9a的普通方程;
(2)设射线eqId417e80f1349244878d01fe90e0891f5feqIdcfc8599bedfb4ab4944abf141f348a9a交于点eqId2381423d4cd146cab95f55527681a766,与eqId3a63d00111554b9e8b896929779a293d交于eqId2efda802d5534f6d92d9f8af7aaec28beqId517584fed25c413ba8b7bb33ffa2d5c6,求eqIdcfb81a24d4b34902a7997513d17fdc96的值.
10 . 已知在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,直线eqId417e80f1349244878d01fe90e0891f5f的参数方程为eqId41b33e93bee146528c6d151ee8dba8aaeqId69f56ef2c88b4b73a560da59f5247a82为参数),以坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b为极点,eqIda9cd3f94eb8045438f75e9daccfa7200轴的非负半轴为极轴建立极坐标系,曲线eqId19a4eb16029e4550a14f2afe4741a3c3的极坐标方程为eqIdbc3a1a420a53407bb3a40dd4cfe300ec,点eqIdbedf755e0fdb4d078d6859360706b163的极坐标是eqId11a80536a15d44ec8e7d2e6e733750d2.
(1)求直线eqId417e80f1349244878d01fe90e0891f5f的极坐标方程及点eqIdbedf755e0fdb4d078d6859360706b163到直线eqId417e80f1349244878d01fe90e0891f5f的距离;
(2)若直线eqId417e80f1349244878d01fe90e0891f5f与曲线eqId19a4eb16029e4550a14f2afe4741a3c3交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,求eqId1efce4fe353e494795a806b4b87f4b1a的面积.
客服 视频 帮助 公众号 官方微信