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解题方法
1 . 已知椭圆
过点
,且有两个顶点所在直线的斜率为
,过椭圆左顶点A的直线l与椭圆C交于点M,与y轴交于点N.
(1)求椭圆C的方程;
(2)若
的面积为
,求直线l的方程;
(3)设过原点O且与直线l平行的直线
交椭圆于点P,求证
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7968194cf13e872ab941231cfc9eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆C的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/101da161ae17652ccbe7d3f888762c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c55e4f3eda94bc505f103b10bc1fee7.png)
(3)设过原点O且与直线l平行的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354f8e9d6cca157b95877d6540d16fb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23939f727e902118ece930f72be086e2.png)
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