1 . 在直角坐标系
中,倾斜角为
的直线
经过坐标原点
,曲线
的参数方程为
(
为参数).以点
为极点,
轴的非负半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)求
与
的极坐标方程;
(2)设
与
的交点为
、
,
与
的交点为
、
,且
,求
值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4151fab0ff51c32c8dd5cbe9f630b3de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cf89e94eb51129f144d9809ec290f7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce395dfb7eab4d1d58a19bce2bfdaf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2019-05-10更新
|
1036次组卷
|
5卷引用:【市级联考】辽宁省丹东市2019届高三总复习质量测试(二)文科数学试题
2 . 选修4-4:坐标系与参数方程
在直角坐标系
中,曲线
的普通方程为
,曲线
参数方程为
(
为参数);以坐标原点
为极点,以
轴正半轴为极轴,建立极坐标系,直线
的极坐标方程为
,
.
(1)求
的参数方程和
的直角坐标方程;
(2)已知
是
上参数
对应的点,
为
上的点,求
中点
到直线
的距离取得最小值时,点
的直角坐标.
在直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8fe0c4c4a65c0132f318a23278a695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd1071b74fe6b968b9ce5bdd48307a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d57678b93f1dcb18d4cbb33ff70bce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2e40c1f1ff5e667d044767de627fff.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc316f251b316a8a62c60017289cc80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2019-04-06更新
|
847次组卷
|
2卷引用:【市级联考】辽宁省丹东市2019届高三总复习质量测试(一)文科数学试题
3 . 在平面直角坐标系
中,曲线
的参数方程为
(
为参数).以
为极点,以
轴正半轴为极轴,建立极坐标系,曲线
的极坐标方程
.
(1)求曲线
的极坐标方程;
(2)设
,
为曲线
上位于
轴上方的两点,且
,射线
,
分别与
相交于点
和点
,当
面积取最小值时,求四边形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764cdc99c64180880e41f25900374f9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629934dbefddc0f1de9a93fb4529074d.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2020-06-16更新
|
469次组卷
|
3卷引用:辽宁省丹东市2020届高三下学期总复习质量测试(二)数学(文)试题
4 . 在直角坐标系
中,将圆
上每一点的横坐标保持不变,纵坐标变为原来的
倍,再把所得曲线上每一点向下平移1个单位得到曲线
.以
为极点,以
轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程是
.
(1)写出
的参数方程和
的直角坐标方程;
(2)设点
在
上,点
在
上,求使
取最小值时点
的直角坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85508b77cdbb9eea6128bfc519667706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef812f839622326a7d7027cc806aaeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a52e26180930ad5b56a8a45f28a0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ecb7ede2088c20b64cd80e906839dbe.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a52e26180930ad5b56a8a45f28a0f2.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a28be4d5a16cf245f6fa7c4088fee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9eeee83b4b7c6ceac7828ff534ce15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a52e26180930ad5b56a8a45f28a0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a1c0a37266a46a94df3a72e0685f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a28be4d5a16cf245f6fa7c4088fee4.png)
您最近一年使用:0次
2018-05-07更新
|
973次组卷
|
2卷引用:【全国市级联考】辽宁省丹东市2018年高三模拟(二)理科数学试题
5 . 在平面直角坐标系
中,曲线
的参数方程为
(
为参数).以坐标原点
为极点,
轴正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)求
的极坐标方程;
(2)将曲线
上所有点的横坐标不变,纵坐标缩短到原来的
倍,得到曲线
,若
与
的交点为
(异于坐标原点
),
与
的交点为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f23bb05e586ec0a3d42bdf95399ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1f08c7640e62e8717abf4d44a6c83.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)将曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c7f91f05a52da791a05d926adbab03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次
6 . 极坐标系的极点为直角坐标系
的原点,极轴为
轴的正半轴,两极坐标系中的长度单位相同.已知曲线
的极坐标方程为
,
.
(1)求曲线
的直角坐标方程;
(2)在曲线
上求一点,使它到直线
:
(
为参数)的距离最短,写出
点的直角坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdebedd02b4ea57f8562443742086d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0ca9a39621967d7ba5629ea9b12d78.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa836f5800641bb7d3b221356b2c0bf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
2017-12-29更新
|
889次组卷
|
7卷引用:辽宁省丹东市五校协作体2018届高三上学期联考数学(文)试卷
2011·辽宁丹东·一模
7 . 选修4—4:坐标系与参数方程.平面直角坐标系中,直线![](https://img.xkw.com/dksih/QBM/2011/7/18/1570265187606528/1570265193283584/STEM/d6ff62ada408487d9d55545fccaa4eb1.png)
的参数方程是
(
为参数),以坐标原点为极点,
轴的正半轴为极轴,建立极坐
标系,已知曲线
的极坐标方程为
.
(Ⅰ)求直线
的极坐标方程;
(Ⅱ)若直线
与曲线
相交于
、
两点,求
.
![](https://img.xkw.com/dksih/QBM/2011/7/18/1570265187606528/1570265193283584/STEM/d6ff62ada408487d9d55545fccaa4eb1.png)
的参数方程是
![](https://img.xkw.com/dksih/QBM/2011/7/18/1570265187606528/1570265193283584/STEM/a93231e34baa4f40943d69cc7586dcd9.png)
![](https://img.xkw.com/dksih/QBM/2011/7/18/1570265187606528/1570265193283584/STEM/7d8c3bf7ec8b49f8b261a5002c5c0b1e.png)
![](https://img.xkw.com/dksih/QBM/2011/7/18/1570265187606528/1570265193283584/STEM/9e98c9664b21446bb678e7463e9c7eb1.png)
标系,已知曲线
![](https://img.xkw.com/dksih/QBM/2011/7/18/1570265187606528/1570265193283584/STEM/2031a8ed589d44179df6423885411eb3.png)
![](https://img.xkw.com/dksih/QBM/2011/7/18/1570265187606528/1570265193283584/STEM/de9dbf65b8c7423099e27fbb76a072d2.png)
(Ⅰ)求直线
![](https://img.xkw.com/dksih/QBM/2011/7/18/1570265187606528/1570265193283584/STEM/d6ff62ada408487d9d55545fccaa4eb1.png)
(Ⅱ)若直线
![](https://img.xkw.com/dksih/QBM/2011/7/18/1570265187606528/1570265193283584/STEM/d6ff62ada408487d9d55545fccaa4eb1.png)
![](https://img.xkw.com/dksih/QBM/2011/7/18/1570265187606528/1570265193283584/STEM/2031a8ed589d44179df6423885411eb3.png)
![](https://img.xkw.com/dksih/QBM/2011/7/18/1570265187606528/1570265193283584/STEM/93d1dce337d146a2abfe0684a9e02fbb.png)
![](https://img.xkw.com/dksih/QBM/2011/7/18/1570265187606528/1570265193283584/STEM/49b8d594bcb84f9baee903a88506668c.png)
![](https://img.xkw.com/dksih/QBM/2011/7/18/1570265187606528/1570265193283584/STEM/28c7bd5740ca477e918a6cf0eaf5ade0.png)
您最近一年使用:0次
2016-11-30更新
|
1166次组卷
|
6卷引用:2012届丹东市四校协作体高三摸底测试数学(零诊) (理)
(已下线)2012届丹东市四校协作体高三摸底测试数学(零诊) (理)(已下线)2012届丹东市四校协作体高三摸底测试数学(零诊) (文)(已下线)2012届海南省高三高考极限压轴卷理科数学试卷(已下线)2013届宁夏银川一中高三第五次月考理科数学试卷2016届黑龙江省哈尔滨师大附中高三12月考文科数学试卷2016届黑龙江省哈尔滨师大附中高三12月考理科数学试卷