1 . 已知椭圆:
的右焦点为F,直线
交椭圆E于M,N两点,若
,短轴的一个端点到直线l的距离是
.
(1)求椭圆E的方程;
(2)已知
的三个顶点都在椭圆上,坐标原点O是
的重心,求证:
的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a93a0f50e7c070a9b03ad051178758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5d51c079d6d326c5fe9d0b79c725524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
(1)求椭圆E的方程;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2 . 已知圆
,A为圆O1上任意一点,点D在线段
上.
,已知
,
.
(1)求点D的轨迹方程H;
(2)若直线
与方程H所表示的图像交于E,F两点,
是椭圆
上任意一点.若OG平分弦EF,且
,
,试判断四边形OEGF形状并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e12caea050eb4d718b3c093d3a4461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d817b898a4106c0fc24edee630a9eed9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/513eafd10fa1ec0196562865517e0b09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365c24c9df47090eddef494e92efcbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a2295b65d38eb6badc08e56aeec329.png)
(1)求点D的轨迹方程H;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebfba7955579ddccf96fe4d912bb2070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e4a41cbe3d1f25154602dee11d36ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2115f612bbd90401bf92628248fadbf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/901ff35410115cf02e32e7e6fc7497a4.png)
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