1 . 已知点P的坐标为
,点Q是参数方程为
(
为参数)的椭圆C上的动点,
(1)求椭圆C的离心率;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcdf9faaba7b7c9b5973c00ef74ef212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(1)求椭圆C的离心率;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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2022-07-09更新
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2卷引用:广西钦州市2021-2022学年高二下学期期末考试数学(理)试题
解题方法
2 . 若以极点为原点,以极轴为x轴正半轴且单位长度相同建立直角坐标系,那么直线
(t为参数)被圆
所截得的弦长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca29b23b54f301a525d87547de6d7d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0ecf60aaca7da8ebd89a554ef5441f2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 若以极点为原点,以极轴为x轴正半轴且单位长度相同建立直角坐标系,直线l的直角坐标方程为
,则极坐标为
的点A到直线l的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48e307be89a2ae01bd3fb8442b4e12af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6d58c8266fc284ecaa48cd9ebb26dee.png)
A.![]() | B.![]() | C.1 | D.3 |
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4 . 在直角坐标系
中,曲线
的参数方程为
(t为参数).在以原点为极点,x轴的正半轴为极轴的极坐标系中,曲线
的极坐标方程为
.
(1)求曲线
和曲线
的直角坐标方程;
(2)设
,若曲线
与曲线
交于A,B两点,求
的值.
![](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/44d5d605a7dea88ccc8ad705c5764bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8230531720914786cf0045bb06c185.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc2de9df8bce6139613bb86322db0f4.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/9486e4e76ff07c6c47091e0e4b8bcd7d.png)
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2022-07-05更新
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3卷引用:广西南宁市部分校2021-2022学年高二下学期期末联考数学(文)试题
5 . 已知曲线
的参数方程为
(其中
),以坐标原点为极点,以
轴的非负半轴为极轴,建立极坐标系,曲线
的极坐标方程为
.
(1)分别求曲线
,
的直角坐标方程;
(2)若曲线
,
相交于
,
两点,求线段
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df0f8bb2a318f38dece8fd09b81d2a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4727ee0a3f2b15b27bfc8bd66ae525c.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/545db5998c4e7525f898c3d8159b6e93.png)
(1)分别求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若曲线
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2022-07-04更新
|
192次组卷
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2卷引用:广西北海市2021-2022学年高二下学期期末教学质量检测数学(理)试题
解题方法
6 . 已知曲线
的参数方程为
(其中
),以坐标原点为极点,以
轴的非负半轴为极轴,建立极坐标系,曲线
的极坐标方程为
.
(1)分别求曲线
,
的直角坐标方程;
(2)若曲线
,
相交于
,
两点,
点为曲线
上的一动点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df0f8bb2a318f38dece8fd09b81d2a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4727ee0a3f2b15b27bfc8bd66ae525c.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/545db5998c4e7525f898c3d8159b6e93.png)
(1)分别求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若曲线
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
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7 . 若直线的参数方程为
(
为参数),则直线的倾斜角为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d845c40f6567f92c74cfa553909ec76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.30° | B.60° | C.120° | D.45° |
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2022-07-04更新
|
334次组卷
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4卷引用:广西北海市2021-2022学年高二下学期期末教学质量检测数学(文)试题
名校
8 . 在极坐标系中,与圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cf89e94eb51129f144d9809ec290f7.png)
不 相切的一条直线的方程是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cf89e94eb51129f144d9809ec290f7.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2022-04-21更新
|
326次组卷
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3卷引用:广西钦州市2021-2022学年高二下学期教学质量监测(期末)数学(文)试题
名校
9 . 过原点作圆
(
为参数)的两条切线,则这两条切线所成的锐角为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde1f282dc5c1154170d85b4b8e11e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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2022-02-22更新
|
348次组卷
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4卷引用:广西钦州市2021-2022学年高二下学期期末考试数学(理)试题
名校
10 . 以直角坐标系的原点
为极点,
轴的非负半轴为极轴建立极坐标系.已知曲线
的极坐标方程为
,倾斜角为
的直线
过点
,点
的极坐标为
.
(1)求曲线
的普通方程和直线
的参数方程;
(2)若
与
交于
,
两点,且点
为
的中点,求点
的极坐标.
![](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/cb7d96c2047d774cc6ca7bef7b915a9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb44db1dc864ff4901be1e10da79747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb44db1dc864ff4901be1e10da79747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eef7056d4a145b7cd11c0afc74d8616.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582bbf355c2f13dde1d69848918603f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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2022-02-19更新
|
837次组卷
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3卷引用:广西百色市2021-2022学年高二下学期期末教学质量调研测试数学(文)试题