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解题方法
1 . 在极坐标系中,曲线C1:ρ=2sinθ,曲线C2:ρ=4cosθ,过极点的直线与曲线C1,C2分别交于异于极点的A,B两点,则|AB|的最大值为( )
A.![]() | B.4 | C.2![]() | D.5 |
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2 . 在直角坐标系
中,曲线C的方程为:
,以O为极点x轴的正半轴为极轴建立极坐标系.
(1)求曲线C的极坐标方程;
(2)直线
的普通方程是
,直线
与曲线C交于O,M两点,与直线
交于点N,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9829c44481108ce4f778a25e39726cf6.png)
(1)求曲线C的极坐标方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4910a1425d7b6bf147f4e5d0b6194b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb56a8e5f7251286dd69b29b0182363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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3 . 在极坐标系中,曲线
关于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0bec2d11edf36de9a6be197756a819.png)
A.直线![]() | B.直线![]() | C.点![]() | D.极点对称 |
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4 . 在极坐标系中,直线
的方程为
,则点
到直线
的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183f6ed8a1b360dd56d66186f077912b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88aee91a16970e80f18624dbc977d0f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 选修4-4:坐标系与参数方程
在平面直角坐标系
中,圆
:
,直线
:
,直线
过点
,倾斜角为
,以原点
为极点,
轴的正半轴为极轴建立极坐标系.
(1)写出直线
与圆
的交点极坐标及直线
的参数方程;
(2)设直线
与圆
交于
,
两点,求
的值.
在平面直角坐标系
![](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/e6316e0e6da742e9b035d8f2cc91a4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc81cfaccc00aa4b7139de5a35a102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879080beb1e55cae2639645cd64c4710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)写出直线
![](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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(2)设直线
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2bdda1b142baeeedabd15e06dfd9ac.png)
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6 . 下列直线中,与曲线
为参数)没有公共点的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a94a19efc9336fafcc8dd7aa7a34e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 已知直线
为参数),以坐标原点为极点,
轴为极轴建立极坐标系,曲线
.
(1)求曲线
的直角坐标方程和直线
的普通方程;
(2)求与直线
平行,且被曲线
截得的弦长为
的直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4ca2dec6defdf203da4666df93c1a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f87a09397dac6d0c2f5c737e8fda561.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求与直线
![](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/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
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8 . 在极坐标系中,直线
与圆
交于A,B两点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d6d69076ca6381d9d401be855e58c79.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8850594bdc157e6aad81cba0011a196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de2d02fb5d7df50538515210f734485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d6d69076ca6381d9d401be855e58c79.png)
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9 . 以坐标原点为极点,
轴正半轴为极轴建立极坐标系,曲线
的极坐标方程为:
,直线
的参数方程为:
(
为参数).
(I)把曲线
的极坐标方程和直线的参数方程化为直角坐标方程;
(II)若直线
与曲线
相交于
两点,求
.
![](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/1bddf0b3db29426b5f1c396736b7f667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9e83df0940114fad164d8eedf92a2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(I)把曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(II)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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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10 . 设
分别为直线
(t为参数)和曲线C:
(
为参数)上的点,则
的最小值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0d7680e1e2b77a0a963ab464fb9671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e1e2aec6fe32ae416f90becb8d227d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a1ee2ea56b649946ca15c7a9ca0755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82358b724051b032c7ec734a226ae84.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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