1 . 椭圆
的右顶点
,过椭圆右焦点的直线l与C交于点M,N,当l垂直于x轴时
.
(1)求椭圆C的方程;
(2)若直线
与y轴交于P点,直线
与y轴交于Q点,点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a98eaaab44a91d0bad21dbd260be770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635f9e9f56bc9e8b5d7ffeb922dba97f.png)
(1)求椭圆C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc1835455f7f683ebc76b2f0e9cc44f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e457b4447d5cf596012e630dd45f16f1.png)
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2 . 已知椭圆C:
与直线
(不平行于坐标轴)相切于点M
,过点M且与
垂直的直线分别交x轴、y轴于A
,,B
两点.
(1)证明:直线
与椭圆C相切;
(2)当点M运动时,点P(m,n)随之运动,求点P的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d12ebd10f6c0bcf98be52c32b107f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6a4781b020b879519321e05c299f6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67c623950b5795d5fb4daeb8102a8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0d834e1f121ec20f2f5a43ac9cd302.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587026a84038002f2f7d4969af4465c6.png)
(2)当点M运动时,点P(m,n)随之运动,求点P的轨迹方程.
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