1 . 已知椭圆C:
过点![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248212234240/1572248218353664/STEM/9b077895fb5e404e8cfa6800a8af29ab.png)
,离心率为
,点
分别为其左右焦点.
(1)求椭圆C的标准方程;
(2)是否存在圆心在原点的圆,使得该圆的任意一条切线与椭圆C恒有两个交点
,且
?若存在,求出该圆的方程;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248212234240/1572248218353664/STEM/9863f99a082549c0830bf8b14f47f227.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248212234240/1572248218353664/STEM/9b077895fb5e404e8cfa6800a8af29ab.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248212234240/1572248218353664/STEM/7f863c7d08db45a2b26dab32b59fe4bc.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248212234240/1572248218353664/STEM/cbb5494aa87f4651ada7b0464b29ca46.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248212234240/1572248218353664/STEM/d76e4fab6af24a0690ecb3f21119b1f2.png)
(1)求椭圆C的标准方程;
(2)是否存在圆心在原点的圆,使得该圆的任意一条切线与椭圆C恒有两个交点
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248212234240/1572248218353664/STEM/b1448a2b752a4c76af673b846a9d1fed.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572248212234240/1572248218353664/STEM/12d6aefd657242399759c80b9e6251d8.png)
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2015-10-08更新
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3卷引用:2014-2015学年黑龙江省龙东南四校高二下期末联考数学(理)试卷