1 . 已知直线l的参数方程为
(t为参数),曲线C的参数方程为
(
为参数),以坐标原点为极点,x轴的正半轴为极轴建立极坐标系,点P的极坐标为
.
(1)求直线l以及曲线C的极坐标方程;
(2)设直线l与曲线C交于A,B两点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de596f9e9dd0d8e5365031e1d6c6ec41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da5cc0f089f609a0d1cbf006a60a75c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50fe6a10c3b9d12c01e362a37b35f18.png)
(1)求直线l以及曲线C的极坐标方程;
(2)设直线l与曲线C交于A,B两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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2017-05-17更新
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2 . 选修4-4:坐标系与参数方程
已知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,
轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(Ⅰ)求曲线
的极坐标方程与曲线
的直角坐标方程;
(Ⅱ)若直线
(
)与曲线
交于
,
两点,求线段
的长度.
已知在平面直角坐标系中,曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa0ece1930473736c506cd3cc82ec6e.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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0cb878349009a779d94b1bc40319bb.png)
(Ⅰ)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(Ⅱ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734a6a1d319648bb969845a9159cdba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f614267fccee84d04f69d6831434a008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](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/7a5f1641947153c80b987320885a2b57.png)
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2017-04-12更新
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3 . 选修4-4:坐标系与参数方程
在直角坐标系
中,直线
,曲线
(
为参数),以坐标原点
为极点,以
轴正半轴为极轴建立极坐标系.
(1)求直线
及曲线
的极坐标方程;
(2)若直线
的极坐标方程为
(
),设
与曲线
的交点为
,求
的面积及
与
交点的极坐标.
在直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb242db36e135e4cb19e87de75bc531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ffe30aab6c756bb838649691175fdfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe211e0dea7a44863e5e1706633c3aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/659e156eaa4aa5369cb6250c958876db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619ab4ea4a7e500c8658b16506015d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94165c5047e68e952df7a8dc6dc32fda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266f65e4f3c47d32014d610419b0215f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
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解题方法
4 . 在直角坐标系
中,圆
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.
(1)求圆
的极坐标方程;
(2)直线
的极坐标方程为
,其中
满足
与
交于
两点,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/c84132a59dcc6ab69ff085f7af59a4b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e8cfb2bc34c87e56be569a8128e9cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c7d6627a568c6eaae35260d53dfb29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b414552245780770283ed603892c26e0.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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2017-03-22更新
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名校
5 . 已知曲线C的极坐标方程是
.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:
(
是参数).
(1)若直线l与曲线C相交于A、B两点,且
,试求实数m值.
(2)设
为曲线
上任意一点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b34a1e7a48f450d883f9a0197e5c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b875c594e93ee8babc7114f392b878c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)若直线l与曲线C相交于A、B两点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ccb4262fe12626c7118f07f9defadc.png)
(2)设
![](https://img.xkw.com/dksih/QBM/2015/3/13/1572007308574720/1572007314702336/STEM/b804aa3c521341e4a6e61b72d5a49de6.png?resizew=56)
![](https://img.xkw.com/dksih/QBM/2015/3/13/1572007308574720/1572007314702336/STEM/f4652d91bbf9490e91cf730d209bb344.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf99adccc80f28343fedd8d0aad7429.png)
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2016-12-03更新
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