1 . 点
为极坐标系中的一点,给出如下各点的坐标:①
;②
;③
;④
.其中可以作为点
关于极点的对称点的坐标的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adc55b3ddd4eb6a59833882cd7f2f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871534be7754c5aa0e44b3883b0781db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bf791b7ef8491139a6a4d32342c670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b93df54612e3a2e5944e9b7c0776f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186fd5251950f62ccba1402ede4f9145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.①② | B.①③ | C.②③ | D.②④ |
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2 . 点
关于极轴的对称点的极坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02be0c4607191680581b703de4c4dda7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 在直角坐标系
中,直线
的参数方程为
(
为参数).以原点
为极点,
轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.点
的直角坐标为
,直线
与曲线
交于
、
两点.
(1)写出点
的极坐标和曲线
的普通方程;
(2)当
时,求点
到两点
、
的距离之积.
![](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/80ec4ec4b327af5ca3338b5045a707aa.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b996d5790cb49cacbc409b8b2e8e3b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f612078b0cdcf31f3c1afa8b0051c8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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)
(1)写出点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c008b0275a602571d8907bb126a563ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
您最近一年使用:0次
4 . 在平面直角坐标系
中,直线
的参数方程为
(
为参数).以坐标原点
为极点,
轴的非负半轴为极轴建立极坐标系,圆
的极坐标方程为
.
(1)求
的普通方程和
的直角坐标方程;
(2)若
与
相交于
,
两点,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/95060febc8c15a97d459c8cf5f70314b.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0eda6b070b030bdaf5752e3525b8aa.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a7002fc4657f8a357802df1a67afe42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c2d5c7a6824bfb6f6cbc98a024eeb2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586053b03d1e8737b6697a6a4016c56.png)
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2022-11-23更新
|
211次组卷
|
2卷引用:江西省西路片七校2023届高三上学期第一次联考数学(文)试题
5 . 在直角坐标系
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
,直线
的极坐标方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ba661d645f716c8b9c73f80f3da026.png)
(1)求:①曲线
的普通方程;
②曲线
与直线
交点的直角坐标;
(2)设点
的极坐标为
,点
是曲线
上的点,求
面积的最大值.
![](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/094ab3a9f3a40f6fc88a4184371dc745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ba661d645f716c8b9c73f80f3da026.png)
(1)求:①曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
②曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880c6f7958454eb391960173b0f83ad4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
您最近一年使用:0次
名校
6 . 极坐标是指在平面内取一个定点O,叫极点,引一条射线
,叫做极轴,再选定一个长度单位和角度的正方向(通常取逆时针方向).对于平面内任何一点M,用
表示线段
的长度,
表示从
到
的角度,有序数对
就叫点M的极坐标.我们经常以坐标原点为极点,x轴正半轴为极轴,从而可以进行直角坐标和极坐标的转化.如直角坐标
的极坐标形式为
,极坐标方程
的直角坐标方程为
.则以下说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd40398a8a965a4ae623a2ab2131a9c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe211e0dea7a44863e5e1706633c3aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281203d3201719fb8d47c399ceeea53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8410a8c1e5ebb292cb6bd4ebc2b77db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8dfc7cd9f30b06fb65c2bb3b211249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b9f330116fcfe8a3ecc13344d609b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192c5142e2d6fccf1ddc6984a635f8f5.png)
A.直角坐标![]() ![]() |
B.极坐标![]() ![]() |
C.直角坐标方程![]() ![]() |
D.极坐标方程![]() ![]() |
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2022-10-20更新
|
401次组卷
|
2卷引用:云南师范大学附属中学2023届高三上学期第四次月考数学试题
名校
7 . 极坐标系中,点
与点
,
表示同一个点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4543c0de8edf386b7a4b005fea2bbde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1bd50946a22b0ee4dab28ecda2df42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f687593cb4ecef31667bf2320fdfe000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
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名校
8 . 如图,在极坐标系Ox中,点
,曲线M是以OA为直径,
为圆心的半圆,点B在曲线M上,四边形OBCD是正方形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/26/b88ebd87-0bb8-44e6-8aa2-fb3c0699cb56.png?resizew=212)
(1)当
时,求B,C两点的极坐标;
(2)当点B在曲线M上运动时,求D点轨迹的极坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390df402040b60fed7f448a15d153899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/26/b88ebd87-0bb8-44e6-8aa2-fb3c0699cb56.png?resizew=212)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56150248dd4b787a2013311e4737e93f.png)
(2)当点B在曲线M上运动时,求D点轨迹的极坐标方程.
您最近一年使用:0次
2022-09-23更新
|
1603次组卷
|
9卷引用:四川省蓉城名校联盟2022-2023学年高三上学期入学联考文科数学试题
四川省蓉城名校联盟2022-2023学年高三上学期入学联考文科数学试题四川省蓉城名校联盟2022-2023学年高三上学期入学联考理科数学试题河南省南阳市第一中学校2022-2023学年高三上学期第二次月考理科数学试题四川省资中县第二中学2022-2023学年高三上学期11月月考理科数学试题宁夏回族自治区银川一中2023届高三第一次模拟考试数学(文)试题宁夏回族自治区银川一中2023届高三第一次模拟考试数学(理)试题广西壮族自治区防城港市2023届高三下学期4月月考数学(文)试题(已下线)专题10-1 极坐标与参数方程题型归类(讲+练)-1陕西省西安市铁一中学2024届高三上学期月考4数学(理)试题
9 . 在极坐标系中,直线
的极坐标方程为
,M是
上任意一点,点P在射线OM上,且满足
,记点P的轨迹为
.则曲线
的极坐标方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ef48f49822d0eabac3bcf416946338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82dc693ff519f8db2afe99bb220eb431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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10 . 极坐标系中一点A的极坐标为
,则点A到极点的距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97fe88412da03cc114f2250593293217.png)
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