1 . 在平面直角坐标系中,直线l的参数方程为
(t为参数).以原点为极点,x轴的非负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的极坐标方程和曲线C的直角坐标方程;
(2)设点
,直线l与曲线C交于点A,B.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2a007d1b907662a60a19aea86c9b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ca9ad42ff37f5a00a7c90b1d96d64.png)
(1)求直线l的极坐标方程和曲线C的直角坐标方程;
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88659e1bac79840020d4494440cfb8e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25346740294b630c2df2a4ac2857de28.png)
您最近一年使用:0次
2023-03-16更新
|
1010次组卷
|
4卷引用:四川省广安市第二中学校2022-2023学年高二下学期期中考试数学试题(文)
2 . 在直角坐标系
中,
是过
且倾斜角为
的一条直线,又以坐标原点
为极点,
的非负半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)写出直线
的参数方程,并将曲线
的极坐标方程化为直角坐标方程;
(2)若直线
与曲线
在
轴的右侧有两个交点
,过点
作
的平行线,交
于
两点,求证:
.
![](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/d5c10f14aae6fb21e047ecb39cdf40c0.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd857fdf83c7bf71883cfdd0c79a13a.png)
(1)写出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0d26766290953a9f5f7ad7791e40b2.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/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f461f01e01ed785cdd10a846b64dd5.png)
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2023-06-01更新
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209次组卷
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4卷引用:内蒙古呼伦贝尔市满洲里市第一中学2022-2023学年高二下学期期末考试文科数学试题
3 . 在平面直角坐标系
中,曲线C的参数方程为
(
为参数),以坐标原点O为极点,x轴的正半轴为极轴,取相同长度单位建立极坐标系,直线l的极坐标方程为
.
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)设直线l与y轴的交点为P,经过点P的动直线m与曲线C交于A,B两点,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87de3ccbef1e3cb0ea5c0e84098f0a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736fc9f625ee6fda2b1b501367427b73.png)
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)设直线l与y轴的交点为P,经过点P的动直线m与曲线C交于A,B两点,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559d66fd8b309fd440ce9bda78a579c9.png)
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2022-07-15更新
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755次组卷
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4卷引用:四川省广安市2021-2022学年高二下学期“零诊”考试数学(理)试题
四川省广安市2021-2022学年高二下学期“零诊”考试数学(理)试题四川省广安市2023届高三零诊文科数学试题(已下线)专题12-1 参数方程与极坐标归类-1四川省绵阳南山中学2024届高三下学期高考仿真演练(一)文科数学试题
解题方法
4 . 在半面直角坐标系中,如果点P的坐标
满足
,其中
为参数.证明:点P的轨迹是圆心为
,半径为r的圆.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f1230127e4acf941aad86aaa216338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
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2021-11-21更新
|
643次组卷
|
5卷引用:人教A版(2019) 选择性必修第一册 新高考名师导学 第二章 2.4 圆的方程
人教A版(2019) 选择性必修第一册 新高考名师导学 第二章 2.4 圆的方程(已下线)2.4 圆的方程(精讲)-2021-2022学年高二数学一隅三反系列(人教A版2019选择性必修第一册)(已下线)2.4 圆的方程(已下线)第11讲 圆与圆的位置关系-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修第一册)人教A版(2019)选择性必修第一册课本习题 习题2.4
名校
5 . 如图,在直角坐标系中,以原点
为极点,
轴正半轴为极轴建立极坐标系.图中的心型曲线
的极坐标方程为
为曲线
上一动点,曲线
的参数方程为
为参数,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/5bd37748-3b01-4e4d-a829-878f30a531b7.png?resizew=155)
(1)若
与
交于
三点,证明:
为定值;
(2)射线
逆时针旋转
后与
交于点
,求
的最大值.
![](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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe4d6fb3e3916b46c2e544eaaba973d5.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/e6a3099c2c948513459151da0dce79f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b463ed27be664efc447bdc4b4aa936.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/5bd37748-3b01-4e4d-a829-878f30a531b7.png?resizew=155)
(1)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/5731a7a079c190e18daa159c67765a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.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/e5784acc1b6ce159c1193b1581eead14.png)
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2022-04-07更新
|
725次组卷
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4卷引用:江西省宜春市上高二中2022届高三5月第十次月考数学(理)试题
江西省宜春市上高二中2022届高三5月第十次月考数学(理)试题陕西省西安中学2022届高三下学期第五次模拟考试理科数学试题(已下线)押全国卷(理科)第22题 坐标系与参数方程-备战2022年高考数学(理)临考题号押题(全国卷)黑龙江省大庆市大庆中学2022届高三第二次模拟数学(理)试题
6 . 如图所示,在平面直角坐标系
中,P是不在x轴上的一个动点,过点P可作抛物线
的两条切线,两切点A、B的连线与
垂直.设直线
与直线
与x轴的交点分别为Q、R.
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815037014687744/2815804218966016/STEM/6577450b-894a-4048-a6d1-ee81f24bcd36.png?resizew=234)
(1)证明:R是一个定点;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815037014687744/2815804218966016/STEM/6577450b-894a-4048-a6d1-ee81f24bcd36.png?resizew=234)
(1)证明:R是一个定点;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50c707d0350c121c6a611db39a5e85d.png)
您最近一年使用:0次
2021-09-25更新
|
625次组卷
|
3卷引用:江西省永新中学2021-2022学年高二上学期期中考试数学(理)试题
名校
7 . 在平面直角坐标系中,P为曲线
(
为参数)上的动点,将P点纵坐标不变,横坐标变为原来的一半得Q点.记Q点轨迹为
,以坐标原点
为极点,
轴非负半轴为极轴建立极坐标系.
(1)求证:曲线
的极坐标方程为
;
(2)
是曲线
上两点,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9d0427cf88f3b650c59cc6778ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.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/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求证:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549ea649efbff82eb432cdcc5cdd73b9.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9faea4deadc69fec42afab055f464340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e651a7faef2db0444fe157613b5779.png)
您最近一年使用:0次
2021-03-06更新
|
1092次组卷
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3卷引用:江西省都昌县第二中学2020-2021学年高二下学期期中考试数学(文)试题
名校
解题方法
8 . 已知直线
为参数,
)经过椭圆
为参数)的左焦点
.
(1)求
的值;
(2)设直线
与椭圆
交于
两点,求
的最小值.
(3)设
的三个顶点在椭圆
上,求证,当
是
的重心时,
的面积是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5869a94f9eb1bf7b6bdccb7d62657204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa59dbbca1330b8095f30ae810772fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1befa136d34a01daa1f93b840991870b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设直线
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0305037a99384cdfe88cb03fbdfe1a.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.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/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
您最近一年使用:0次
名校
9 . 设
为坐标原点,椭圆
:
经过升缩变换
后变为曲线
,
是曲线
上的点.
(1)求曲线
的方程.
(2)设点
在直线
上,且
.证明:过点
且垂直于
的直线
过
的左焦点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfa06467d100acf800b4d5fbe72d08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d7896d03df0abed59cc696526e1ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.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/a0ed1ec316bc54c37c4286c208f55667.png)
您最近一年使用:0次
10 . 在平面直角坐标系中,曲线
的参数方程为
(
为参数).以原点
为极点,
轴的非负半轴为极轴建立极坐标系,直线
的极坐标为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7cab5a7fcb6721b34b7a2aa6df13de2.png)
(1)求曲线
的普通方程与直线
的直角坐标方程;
(2)设直线
与曲线
交于
两点,点
的坐标为
,证明:直线
关于
轴对称.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd494adc8e1ca5cc8613069218f97c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152236216f8d1cb39b261108e8fc8b9e.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/c7cab5a7fcb6721b34b7a2aa6df13de2.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
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9卷引用: 四川省仁寿县文宫中学2021-2022学年高二下学期期中考试数学(文科)试卷
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