1 . 已知椭圆的极坐标方程为
,求椭圆焦距和长轴长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb0332d6d07ce81c98405ed3523acbf.png)
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2 . 求圆心为
,半径为
的圆的极坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b6dea02ce73af7466b13d0b3243fe03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 圆心C的极坐标为
,且圆C经过极点.
(1)求圆C的极坐标方程;
(2)求过圆心C和圆与极轴交点(不是极点)的直线的极坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fda16b497a07e8f8db97074ec19b35.png)
(1)求圆C的极坐标方程;
(2)求过圆心C和圆与极轴交点(不是极点)的直线的极坐标方程.
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4 . 在极坐标系中,直线
的极坐标方程为
,M是
上任意一点,点P在射线OM上,且满足
,记点P的轨迹为
.则曲线
的极坐标方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ef48f49822d0eabac3bcf416946338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82dc693ff519f8db2afe99bb220eb431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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5 . 极坐标方程分别是
和
的两个圆的圆心距为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0cb878349009a779d94b1bc40319bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdebedd02b4ea57f8562443742086d3.png)
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解题方法
6 . 在直角坐标系xOy中,曲线
:
(
为参数,
),其中
,在以O为极点,x轴正半轴为极轴的极坐标系中,曲线
:
,
:
.若
、
相交于点A,
、
相交于点B,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb71edf8424b30fd942f5316cdad638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10adc3992efb2badc23f81d36faa206f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdebedd02b4ea57f8562443742086d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b80024f36b7b8604522ba11a6ca129.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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7 . 已知在极坐标系中,O为极点,圆C的极坐标方程为
,点P的极坐标为
,求△OCP的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd8dc7c8ad282702a925c291fee3ecda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d63ac244b1cf9332bbe2eb1a94492bf.png)
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8 . 已知曲线的极坐标方程分别为
:
,
:
,其中
,
,求曲线
、
交点的极坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6fe64775315318a236bd8865ac3a09e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b34a1e7a48f450d883f9a0197e5c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278949a1dbbe742ef4dfb4596fd94911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e50e70b144bae8fa026a41488da3b90b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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9 . 在直角坐标系xOy中,以O为极点,x轴正半轴为极轴建立极坐标系,P的直角坐标为
,则直线OP的极坐标方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db92cef1cb821fd592530f4971d27e9.png)
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10 . 在极坐标系中,已知点
在直线
:
上,(其中
,
).![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62bb325f5dbc8967ca91a227723c7ec8.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7584ce6e74ecb0f2c1a5019360d42b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1d992d70f08aa87aa83bafa65fde6d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278949a1dbbe742ef4dfb4596fd94911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eec3e684af41f9ed4db5b931b9ccfb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62bb325f5dbc8967ca91a227723c7ec8.png)
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