名校
1 . 已知曲线C的极坐标方程是ρ= 4cosθ.以极点为平面直角坐标系的原点,极轴为x轴的正半轴,建立平面直角坐标系,直线l的参数方程是
(t是参数).
( I)将曲线C的极坐标方程化为直角坐标方程;
( II)若直线,与曲线C相交于A、B两点,且|AB|=
,求直线的倾斜角a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b43ec977983f1f24750dcc39c059ba5.png)
( I)将曲线C的极坐标方程化为直角坐标方程;
( II)若直线,与曲线C相交于A、B两点,且|AB|=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01961669cd597f61fa48e9853d678bb8.png)
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22卷引用:2017届广东省汕头市高三第一次模拟考试数学(文)试卷
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2 . 选修4-4:坐标系与参数方程
在平面直角坐标系
中,以原点为极点,
轴正半轴为极轴建立极坐标系.已知曲线C的极坐标方程是:
,曲线D的参数方程是:
(
为参数)
(1)求曲线C与曲线D的直角坐标方程;
(2)若曲线C与曲线D相交于A、B两点,求|AB|.
在平面直角坐标系
![](https://img.xkw.com/dksih/QBM/2016/10/16/1573072174120960/1573072180338688/STEM/5ac3391468d34bfc8209527c1a73fdc3.png)
![](https://img.xkw.com/dksih/QBM/2016/10/16/1573072174120960/1573072180338688/STEM/16ffc463fda6415981f6f9552be47fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937763be8c467fe0f2442fdfa3d82785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07911db86b8e09935f0008d26f8b9fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d1a34ae2b8c77f8d7e355c6d1d667e.png)
(1)求曲线C与曲线D的直角坐标方程;
(2)若曲线C与曲线D相交于A、B两点,求|AB|.
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名校
3 . 选修4-4:坐标系与参数方程
已知曲线
的极坐标方程是
,以极点为平面直角坐标系的原点, 极轴为
轴的正半轴建立平面直角坐标系, 若倾斜角为
的直线
经过点
.
(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
交于不同的两点
、
,求
的值.
已知曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f07a3dc0e3632a7d2f32858f7003b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdab625e32e38d1c72c901cece0e147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c3cd0f97c1b6006246d073e888280b.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64f462ecd931af7043e4cf3f8758f45.png)
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名校
4 . 在平面直角坐标系
中,
点的直角坐标为
(
为参数).在以原点
为极点,
轴正半轴为极轴的极坐标中,直线
的极坐标方程为
.
.
(1)试求出动点
的轨迹方程(用普通方程表示)
(2)设
点对应的轨迹为曲线
,若曲线
上存在四个点到直线
的距离为1,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/301a0fc5746ae6c503d46ae6089fed38.png)
![](https://img.xkw.com/dksih/QBM/2016/4/12/1572591534325760/1572591540781056/STEM/f7be550506074d30bcdb6117c0b58cd0.png)
![](https://img.xkw.com/dksih/QBM/2016/4/12/1572591534325760/1572591540781056/STEM/4acd7b8b06524d62a7211aecf72790ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d1a34ae2b8c77f8d7e355c6d1d667e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81574a3738c0a314293ff7c74248971.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/f0aa38b10bd1c0d0dcafefa242353f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578952449f2ae86fd5c1e239e602b170.png)
(1)试求出动点
![](https://img.xkw.com/dksih/QBM/2016/4/12/1572591534325760/1572591540781056/STEM/f7be550506074d30bcdb6117c0b58cd0.png)
(2)设
![](https://img.xkw.com/dksih/QBM/2016/4/12/1572591534325760/1572591540781056/STEM/f7be550506074d30bcdb6117c0b58cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca66a268d6f46e0e9d5d9151b785be60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca66a268d6f46e0e9d5d9151b785be60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2016-12-04更新
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5 . (坐标系与参数方程选做题)若以直角坐标系的
轴的非负半轴为极轴,曲线
的极坐标系方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a909df442c196074eb980d1f4e21b245.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af19cfb4b649e8c9b85b9988c04533c1.png)
,直线
的参数方程为
(
为参数),则
与
的交点A的直角坐标是___________ .
![](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/a909df442c196074eb980d1f4e21b245.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af19cfb4b649e8c9b85b9988c04533c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a4a0da075365acdf06cc968ee3c25c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19d5779cf54485b9acff014d9b62d947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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解题方法
6 . (极坐标与参数方程选讲选做题)已知两曲线的参数方程分别为
(
为参数)和
(
为参数),则它们的交点坐标为 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80971a17d0279dfac65cc1921468a92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5764f6c61decbba3d8956abcd1a9e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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解题方法
7 . 已知直线
的参数方程为
(
为参数),曲线
的极坐标方程为
,点
是直线
上的一个动点,过点
作曲线
的切线,切点为
,则
的最小值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f078ba2bbd55706922d03f871993c45.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/094ab3a9f3a40f6fc88a4184371dc745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82358b724051b032c7ec734a226ae84.png)
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8 . (坐标系与参数方程选做题)曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319bdd02464019827584973e66e9b8ab.png)
(
为参数),若以点
为极点,
轴正半轴为极轴建立极坐标系,则该曲线的极坐标方程是 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319bdd02464019827584973e66e9b8ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54df5475e4f9d6f6d054b053e167246b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d1a34ae2b8c77f8d7e355c6d1d667e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0b35172dc22c88e496413fb018d4d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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9 . (坐标系与参数方程选做题)在极坐标系中,曲线
与
的方程分别为
与
,以极点为平面直角坐标系的原点,极轴为
轴的正半轴,建立平面直角坐标系,则曲线
与
交点的直角坐标为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3818e95641a272c1616f0cbd838c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2634cca127c335b9f66d88ccfb22d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb15f2fd50140255595b188b6ffa75c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f11b5220813e96b65c9af4b5de0f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3818e95641a272c1616f0cbd838c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2634cca127c335b9f66d88ccfb22d165.png)
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10 . (坐标系与参数方程选做题)已知直线
的方程是
(
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,圆
的极坐标方程为
,则圆
上的点到直线
的距离的最小值是 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ef2d80d35da6ee059567fa3ef92d00.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/ca66a268d6f46e0e9d5d9151b785be60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2da02db31d3c74f50e0b44d9f105fe97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca66a268d6f46e0e9d5d9151b785be60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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