18-19高二上·广东惠州·期末
1 . (本小题满分12分)
如图,椭圆的左焦点为
,过点
的直线交椭圆于
,
两点.当直线
经过椭圆的一个顶点时,其倾斜角恰为60°.
(1)求该椭圆的离心率;
(2)设线段的中点为
,
的中垂线与
轴和
轴分别交于
,
两点.记△
的面积为
,△
(
为原点)的面积为
,求
的取值范围.
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2 .
已知椭圆
两个焦点的坐标分别是
,
,并且经过点
.
(1)求椭圆
的标准方程;
(2) 已知
是椭圆
的左顶点,斜率为
的直线交椭圆
于
,
两点,
点
在
上,
,
,证明:
.
已知椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6c61748fc3818d8cabeccba16fc3a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2) 已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be6cf733cfbe1c8e9c0b6a8a879246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3342ceb71dc21a5e6150caad2ce0b029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90529857405acf082f1212ed34256802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c743d555096ef027592cf07c092189f1.png)
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