14-15高二上·江西赣州·期末
解题方法
1 . 如图,椭圆
过点
,其左、右焦点分别为
,离心率
,M,N是直线x=4上的两个动点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/7bbdf286-b86b-4c41-a664-41fc84e85cf1.png?resizew=206)
(1)求椭圆的方程;
(2)求|MN|的最小值;
(3)以MN为直径的圆C是否过定点?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea21bc3f7c77a352c7afa862fc94db4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/7bbdf286-b86b-4c41-a664-41fc84e85cf1.png?resizew=206)
(1)求椭圆的方程;
(2)求|MN|的最小值;
(3)以MN为直径的圆C是否过定点?请证明你的结论.
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