2010·湖南长沙·一模
1 . 设椭圆
的左、右焦点分别为F1与
F2,直线
过椭圆的一个焦点F2且与椭圆交于P、Q两点,若
的周长为
.
(1)求椭圆C的方程;
(2)设椭圆C经过伸缩变换
变成曲线
,直线
与曲线
相切
且与椭圆C交于不同的两点A、B,若
,求
面积的取值范围.(O为坐标原点)
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/18d781d8551743eb85e594ab52c22ca7.png)
F2,直线
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/7c515639ebc0463da322350cec2abbff.png)
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/b33b7697e94a44ecb3d1b2a18535f796.png)
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/c7a38f6d2b434726a9cb97aafdaf6375.png)
(1)求椭圆C的方程;
(2)设椭圆C经过伸缩变换
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/09e7d3d47a3c48fea0da11229ddc0e7d.png)
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/ffccad7eba3845e498402a77d8be747e.png)
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/77ace84b00ad4ac9b8d2a69db2b0521a.png)
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/ffccad7eba3845e498402a77d8be747e.png)
且与椭圆C交于不同的两点A、B,若
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/8838660c4ba34cb5a4cec45453b27c82.png)
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/e32d9c4167a949778f2b219c01f01f7d.png)
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