1 . 已知直线
的参数方程为:
(
为参数),以平面直角坐标系xOy的原点O为极点,x轴的正半轴为极轴,取相同的长度单位建立极坐标系,曲线C的极坐标方程为
.
(1)求直线
和曲线C的普通方程;
(2)在直角坐标系中,过点B(0,1)作直线
的垂线,垂足为H,试以
为参数,求动点H轨迹的参数方程,并指出轨迹表示的曲线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/286cd79bb624634b1586dc73fbbb1e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92bd4f1f65930f3d543a2eb582807b38.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)在直角坐标系中,过点B(0,1)作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ed74dbeba7d418a559f9c97c1df414.png)
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2014·安徽芜湖·二模
解题方法
2 . 在平面直线坐标系XOY中,给定两点A(1,0),B(0,-2),点C满足
,且
.
(1)求点C的轨迹方程.
(2)设点C的轨迹与双曲线
(
)相交于M,N两点,且以MN为直径的圆经过原点,求证:
是定值.
(3)在(2)条件下,若双曲线的离心率不大于
,求该双曲线实轴的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69baa2692da8eab9cb9259c3d2b04378.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048745938798b407c1dac9b3c48a0b8f.png)
(1)求点C的轨迹方程.
(2)设点C的轨迹与双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80235d30a95d6cf370a71589ba2101d8.png)
(3)在(2)条件下,若双曲线的离心率不大于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
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