名校
1 . 在平面直角坐标系
中,以原点O为极点,x轴正半轴为极轴建立极坐标系,已知曲线
.与曲线
相交于P,Q两点.
(1)写出曲线
的直角坐标方程,并求出
的取值范围;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7c760760707461b47f94c7ce047fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef710f508a67379997fcfe023a96796.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f98028327ccdd08aa8374f20257ff143.png)
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6卷引用:江西省萍乡市2023届高三上学期期末考试数学(文)试题
2 . 在平面直角坐标系
中,曲线
的参数方程为:
(
为参数),在以
为极点,
轴的非负半轴为极轴的极坐标系中,点
的极坐标为
.
(1)写出曲线
的普通方程,并判断点
与曲线
的位置关系;
(2)设直线
:
与曲线
交于
两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b03d0ecf7c08dc31ef8ccf4b16397ff.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44812068e46ef58b4ed17b7fc48917a5.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83291940297935d235f71652017cc327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f4d64cb239c5d3e42bbb6fd0c7f469.png)
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5卷引用:江西省宜春市2021-2022学年高二下学期期末质量检测数学(理)试题
解题方法
3 . 曲线
的参数方程为
(
为参数),则曲线
的普遍方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646919fe5ceab00c4cc7fd226ff3e22c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-06-30更新
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3卷引用:江西省吉安市2021-2022学年高二下学期期末教学质量检测数学(文)试题
4 . 在平面直角坐标系xOy中,曲线
的参数方程为
,(t为参数),以坐标原点O为极点,x轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)求曲线
的普通方程和曲线
的直角坐标方程;
(2)已知
,曲线
与曲线
相交于A,B两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4744c903f31a51de0adbdb87816ea83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef57c84b5636205ba7d3a31d1e16b7c1.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559d66fd8b309fd440ce9bda78a579c9.png)
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2022-02-21更新
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902次组卷
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5卷引用:江西省南昌市八一中学、洪都中学、南师附中、十七中四校2021-2022学年高二上学期期末联考数学(文)试题
江西省南昌市八一中学、洪都中学、南师附中、十七中四校2021-2022学年高二上学期期末联考数学(文)试题(已下线)解密23 坐标系与参数方程 (讲义)-【高频考点解密】2022年高考数学(理)二轮复习讲义+分层训练(全国通用)宁夏六盘山高级中学2022届高三第一次模拟考试数学(理)试题(已下线)二轮拔高卷03-【赢在高考·黄金20卷】备战2022年高考数学(文)模拟卷(全国卷专用)陕西省咸阳市高新一中2022-2023学年高三上学期第五次质量检测理科数学试题
5 . 直线
(t为参数)被圆
所截得的弦长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c2e080e13559c2ed5d2c9d31399d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0ecf60aaca7da8ebd89a554ef5441f2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-02-21更新
|
925次组卷
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2卷引用:江西省南昌市八一中学、洪都中学、南师附中、十七中四校2021-2022学年高二上学期期末联考数学(文)试题
名校
6 . 在平面直角坐标系
中,圆C的参数方程为
(
为参数),直线l的参数方程为
(t为参数),设原点O在圆C的内部,直线l与圆C交于M,N两点;以O为极点,x轴的正半轴为极轴建立极坐标系.
(1)求直线l和圆C的极坐标方程,并求a的取值范围;
(2)求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/513ab96d9b0704728f0f15c1186a63d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9f6ea18207d6f880b28ae20fbdf832.png)
(1)求直线l和圆C的极坐标方程,并求a的取值范围;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4de13a47637548ce5594ed8d64dec0c.png)
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|
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|
3卷引用:江西省吉安市2022届高三上学期期末数学(文)试题
7 . 以直角坐标系的原点
为极点,
轴的正半轴为极轴建立极坐标系,已知直线
的极坐标方程为
,曲线
的参数方程是
(
为参数
.
(1)求直线
和曲线
的普通方程;
(2)直线
与
轴交于点
,与曲线
交于
,
两点,求
.
![](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/b483a744ac7f8cb76fc32455e2e2aa9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8eafd55aec7b6aa88b54735488fb885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/2222b7c88dee144e52f3c96738a49fe2.png)
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8 . 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)求曲线
的普通方程和曲线
的直角坐标方程;
(2)若
与
相交于A、
两点,设
,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/755654cb5087c4cdaf0e240319b3ffed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.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/55e30290bbee8339a99382e2b11efdfe.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d26e5a4e3472fd6b1dbc1ea628a3fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3979f27823cdcba516dfa885d8afe19d.png)
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2022-02-21更新
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605次组卷
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3卷引用:江西省南昌市湾里一中等六校2021-2022学年高二上学期期末数学(文)试题
江西省南昌市湾里一中等六校2021-2022学年高二上学期期末数学(文)试题(已下线)解密23 坐标系与参数方程(分层训练)-【高频考点解密】2022年高考数学二轮复习讲义+分层训练(全国通用)北京市昌平区新学道临川学校2021-2022学年高二下学期期中考试数学试题
9 . 在直角坐标系
中,直线
的参数方程为
(
为参数).以原点O为极点,x轴的正半轴为极轴建立极坐标系,曲线C的极坐标方程为
.
(1)求直线
的普通方程,曲线C的直角坐标方程;
(2)设直线
与曲线C相交于A,B两点,点
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18892bfda70920d49255b6d2a87a4190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c6521dbc53f1e10808f0f7ec2a14ae2.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57584ee64ad169908584b55ba7ceaa9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892f57757d6b80b89d8df9449302057d.png)
您最近一年使用:0次
10 . .在直角坐标系
中,点
,直线
的参数方程为
(
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,已知曲线
的极坐标方程为
,直线
与曲线
相交于A,B两点.
(1)求曲线
的直角坐标方程和直线
的普通方程;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048dbcb679f8a85480f73e96b09124af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c603ce77eefb9bf55e6e1cad7fb225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7ade0c538c7cb62ebeeac3605c7f12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c65256eb10d257a6693e72a9c3f9579.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次