1 . 平面直角坐标系中,直线l的参数方程为
(t为参数),以坐标原点O为极点,x轴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l的普通方程和曲线C的直角坐标方程;
(2)设点
,直线l交曲线C于A,B两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32a753e059b81bf840c4a60045fb0ecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/408c977e242c5500f384acf957d5471d.png)
(1)求直线l的普通方程和曲线C的直角坐标方程;
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacfc149ede71417fa599c21b5a84cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063f4f4ce1d9822e9d5144ca0fc83979.png)
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2022-02-04更新
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3卷引用:安徽省芜湖市2021-2022学年高三上学期期末文科数学试题
名校
2 . 在极坐标系中,点
到直线
的距离为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce1a60188db1d28db815a3b074fb82f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c6019a213eca9f791d21a1677dd9f6.png)
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3 . 将下列曲线的极坐标方程化为直角坐标方程
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cf89e94eb51129f144d9809ec290f7.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e7fe7d70daba5a42a28596b1a4a498.png)
(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a40d2cf43fce0c99dff3470d554eb8.png)
(4)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094ab3a9f3a40f6fc88a4184371dc745.png)
(5)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cf89e94eb51129f144d9809ec290f7.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e7fe7d70daba5a42a28596b1a4a498.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a40d2cf43fce0c99dff3470d554eb8.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094ab3a9f3a40f6fc88a4184371dc745.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a943b91bf0461309b8515daac297151c.png)
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4 . 在直角坐标系
中,曲线
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,射线
的极坐标方程为
(
),射线
的极坐标方程为
.
(1)指出曲线
的曲线类型,并求其极坐标方程;
(2)若射线
与曲线
交于
,
两点,射线
与曲线
交于
,
两点,求
的面积的取值范围.
![](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/98afaeaf61b8dc19027931e3364ceb9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f5d2e8186f0173d7862b1d39fb3dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b495a7a39cd372ac8aa24132c4459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d258ec168bfd84bda8ea26ce6e909b.png)
(1)指出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
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河南省天一大联考2020-2021学年高二下学期期中考试文科数学试题河南省濮阳市2020-2021学年高二下学期期中数学文科试题宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(文)试题(已下线)宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(文)试题
5 . 在直角坐标系
中,已知椭圆
的参数方程为
(
为参数),直线
的参数方程为
(
为参数),直线
垂直与直线
且过椭圆
的右焦点为
.
(1)求椭圆
的普通方程和直线
的参数方程;
(2)直线
交椭圆
于
,
两点,求
.
![](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/0163a6460d2f5e04753e719145e1ae5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a9df9d05947cee6b70c5613f769061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)直线
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bece4bb3068ac3b5f9c875f1111c24.png)
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名校
6 . 将曲线
变换为曲线
的一个伸缩变换为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7eff4b85f4eb7a84d323e0848bcfd20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89445182379c738967c2772bc1eb11f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-06-22更新
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4卷引用:河南省郑州市2020-2021学年高二下学期期末数学文科试题
河南省郑州市2020-2021学年高二下学期期末数学文科试题甘肃省高台县第一中学2021-2022学年高二下学期3月月考数学(文科)试题甘肃省会宁县第一中学2021-2022学年高二下学期期中考试数学(文)试题(已下线)第五篇 向量与几何 专题3 仿射变换与反演变换 微点5 仿射变换综合训练
名校
7 . 已知在平面直角坐标系
中,以坐标原点为极点,以
轴的非负半轴为极轴,且取相同的单位长度建立极坐标系,曲线
的极坐标方程为
,曲线
的极坐标方程为
,曲线
交曲线
于
,
两点.
(1)求曲线
与曲线
的直角坐标方程;
(2)试判断曲线
与曲线
公共点的个数.
![](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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f182c46aa2e745f5ac6d9420ed737976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885995a56b79f6c8c73224dc9d61b47.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)试判断曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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2021-06-18更新
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3卷引用:内蒙古包头市第六中学2020-2021学年高二下学期期中考试数学(文)试题
8 . 已知圆
的极坐标方程为
,直线l的参数方程为
(
为参数).
(1)把圆C的极坐标方程化为直角坐标方程;
(2)求直线l被圆
截得的线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c05cf382bac1536c74666819e4da1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2541bd9675ff3ef6723b06d084316c9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)把圆C的极坐标方程化为直角坐标方程;
(2)求直线l被圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2020-07-01更新
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2卷引用:广西北流市实验中学2019-2020学年高二下学期期中考试数学(文)试题
9 . 将下列曲线的极坐标方程化为直角坐标方程
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cf89e94eb51129f144d9809ec290f7.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e7fe7d70daba5a42a28596b1a4a498.png)
(3)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cf89e94eb51129f144d9809ec290f7.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e7fe7d70daba5a42a28596b1a4a498.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734a6a1d319648bb969845a9159cdba7.png)
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解题方法
10 . 已知曲线
的极坐标方程为
,曲线
的参数方程为
(
为参数).
(1)求曲线
,
的普通方程并指出它们的形状;
(2)若点
在曲线
上,点
在曲线
上,求线段
长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d8c71346c65c7a17ceba313f79fbc04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05f56a6a47f30708a1c6c789b76eeda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2020-06-04更新
|
632次组卷
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3卷引用:河南省开封市五县联考2019-2020学年高二下学期期中考试数学(文)试题