解题方法
1 . 已知椭圆
的左、右焦点分别是
,
,动直线l与椭圆C有且只有一个公共点P(点P在第一象限),且与x,y轴分别交于G,E两点,过点P作直线l的垂线分别交x,y轴于M,H,过点
,H的直线交椭圆C于A,B两点.记
,
,
的面积分别为
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/2/1/2648879660310528/2649500821340160/STEM/02655851-ff22-402d-96f5-69420fc09146.png)
(Ⅰ)求证:
为定值;
(Ⅱ)是否存在点P,使得
? 如果存在,写出一个点P的坐标即可;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69daca955a565fa537347dd0d93783f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d237847bcdd6c7d322ae1089e9322429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b49bd8eb3074ba6181dabd9c1ea206a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://img.xkw.com/dksih/QBM/2021/2/1/2648879660310528/2649500821340160/STEM/02655851-ff22-402d-96f5-69420fc09146.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f885faac5a2f2bc286ae08143deaa2.png)
(Ⅱ)是否存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921453160585a55bef915aa02395a452.png)
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