名校
解题方法
1 . 在直角坐标系中,直线
的参数方程为
(
为参数),曲线
的参数方程为
(
为参数).
(1)求直线
和曲线
的直角坐标方程;
(2)若直线
与曲线
相交弦的中点坐标为
,求直线
的极坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43500d286e414bcfd78c1fb379d4626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553ec7e59f9e5b472fed2f3191972423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(1)求直线
![](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/5d0924ff22fff9f5639feb0ceeece80d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2023-11-23更新
|
434次组卷
|
3卷引用:西藏拉萨市城关区拉萨中学2024届高三第五次月考数学(文)试题
解题方法
2 . 在平面直角坐标系
中,曲线
的参数方程为
(其中
为参数).以坐标原点为极点,
轴非负半轴为极轴建立极坐标系,直线
的极坐标方程为
.
(1)求直线
的直角坐标方程和曲线
的普通方程;
(2)设直线
与曲线
交于
,
两点,求线段
的长度.
![](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/db9ad0264a9f70324d53ebbcd38fbd35.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0c51ea8679f02108d04c6cddfd23c30.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
3 . 以等边三角形的每个顶点为圆心,以其边长为半径,在另两个顶点间作一段圆弧,三段圆弧围成的曲边三角形被称为勒洛三角形.如图,以极点O为直角坐标原点,极轴
为x轴正半轴建立平面直角坐标系
.在极坐标系
中,曲边三角形
为勒洛三角形,且
.由已知曲线C的参数方程为
(t为参数).
(1)求
的极坐标方程与曲线C的普通方程;
(2)求曲线C与
交点的极坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6c71a0da6a878a5b12bf8a8e784645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fdd9f5d8efc6cdf97d90f786f897fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666148c5d4bf9c46b081e22b709dcb76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/22/2e60f1d0-6351-4fb6-ab7a-d3950f8d703e.png?resizew=158)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320c0f9263761963de27e41442a62a42.png)
(2)求曲线C与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320c0f9263761963de27e41442a62a42.png)
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2023-07-21更新
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229次组卷
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3卷引用:西藏日喀则市2023届高三第一次联考模拟数学(文)试题
名校
解题方法
4 . 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,
轴的正半轴为极轴建立极坐标系,直线
的极坐标方程是
.
(1)求曲线
的直角坐标方程和直线
的普通方程;
(2)若
,直线
与曲线
交于
两点,
是线段
的中点,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/3dedc90538c22f5613831d0276ad5890.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/c73394b161c18674bcfd056f97069ff3.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bab45799f9f8d0374f529e8b30a0b27.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b718bf34be5b7dabf0b32f10faead104.png)
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2023-05-20更新
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1439次组卷
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11卷引用:西藏林芝市第二高级中学2023届高三第四次模拟考试数学(理)试题
西藏林芝市第二高级中学2023届高三第四次模拟考试数学(理)试题河南省驻马店市2023届高三二模理科数学试题四川省南江中学2023届高三下学期五月适应性考试(一)理科数学试题四川省南江中学2023届高三下学期五月适应性考试(一)文科数学试题贵州省2023届高三多校联考数学(文)试题陕西省西安市西咸新区泾河新城第一中学2022-2023学年高二下学期5月质量检测理科数学试题四川省绵阳市高中2024届高三突击班第零次诊断性考试理科数学试题河南省创新发展联盟2023届高三仿真模拟预测理科数学试题河南省驻马店市2023届高三第二次联考文科数学试题河南省创新发展联盟2023届高三高考仿真模拟预测文科数学试题四川省绵阳市三台中学校2024届高三下学期第一次仿真测试理科数学试题
名校
5 . 在直角坐标系xOy中,曲线C的参数方程为
(
为参数),以坐标原点O为极点,x轴的正半轴为极轴建立极坐标系,直线l的极坐标方程为
.
(1)求C和l的直角坐标方程;
(2)求C上的点到l距离的最小值.
![](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/aa7ee7dce82929e9f332573b6f30e23f.png)
(1)求C和l的直角坐标方程;
(2)求C上的点到l距离的最小值.
您最近一年使用:0次
2023-05-18更新
|
351次组卷
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4卷引用:西藏林芝市第二高级中学2024届高三上学期第一次月考数学(文)试题
6 . 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,直线
的极坐标方程为
.
(1)求曲线
的普通方程与直线
的直角坐标方程;
(2)设
、
分别为曲线
和直线
上的任意一点,求
的最小值.
![](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/cea9a8ef5e0327f2d062ca5a49d3dcea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.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/df410d824214f11a11fba4cae0dbc704.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
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](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/d44e8bc37ed03f44470762748a8f942a.png)
您最近一年使用:0次
2023-04-18更新
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3卷引用:西藏拉萨市2023届高三一模数学(理)试题
21-22高三上·上海浦东新·期中
名校
解题方法
7 . 已知圆
的圆心为
,则点
到直线
(
为参数)的距离为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd767240a603ca0c0db5567707eb704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ffe595a7661f0d5ed788827814d2c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2023-01-29更新
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4卷引用:西藏林芝市第二高级中学2024届高三上学期第三次月考数学(理)试题
西藏林芝市第二高级中学2024届高三上学期第三次月考数学(理)试题(已下线)上海市华东师范大学第二附属中学2022届高三上学期期中数学试题上海市杨浦高级中学2023-2024学年高二上学期期中数学试题(已下线)2.5 曲线与方程(五大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
解题方法
8 . 圆
的参数方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a40f60a5bf3faee549f270a3cd97dd.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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2022-12-31更新
|
288次组卷
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2卷引用:西藏林芝市第二高级中学2022-2023学年高二下学期期末考试数学(文)试题
9 . 在直角坐标系
中,曲线
的参数方程为
(
为参数).以
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
.
(1)求曲线
的普通方程和曲线
的直角坐标方程;
(2)求曲线
的任意一点到曲线
距离的最小值.
![](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/e10b2a16418f5fa81374e41c96c6c075.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/ad93f30d3d1df9f2c5712cbbad9bda7f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
您最近一年使用:0次
2022-12-26更新
|
1283次组卷
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5卷引用:西藏林芝市第二高级中学2024届高三上学期第二次月考数学(文)试题
10 . 在直角坐标系xOy中,曲线
的方程为
(
为参数),以坐标原点为极点,x轴正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)求
的普通方程;
(2)求
的直角坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dffbb12fce69628e7472100b2fd90762.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/293bcfd0679b28bea188755ae9c10d9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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