题目
题型:不详难度:来源:
椭圆G:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185421-27649.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185421-94723.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185421-74771.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185422-39794.gif)
(1)求离心率
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185422-67245.gif)
(2)当离心率
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185422-67245.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185422-69936.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185422-90499.gif)
①求此时椭圆G的方程;
②设斜率为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185422-39776.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185423-49844.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185423-68022.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185423-62563.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185422-39776.gif)
答案
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185423-68842.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185424-68593.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185424-30428.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185424-47878.gif)
(2)①当离心率的
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185424-30428.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185424-15494.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185425-21538.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185425-86148.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185425-64222.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185425-73193.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185425-10636.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185426-65398.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185426-13491.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185426-20744.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185426-54717.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185427-62323.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185427-64098.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185427-41046.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185426-13491.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185427-66949.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185428-58922.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185428-69172.gif)
∴所求椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185423-68842.gif)
②设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185428-84599.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185428-53646.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185428-43944.gif)
又直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185429-24393.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185423-68022.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185429-24393.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185429-20891.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185429-13880.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185429-14892.gif)
由①②解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185430-50667.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185430-53725.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185430-72914.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185430-13231.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185430-22568.gif)
故当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185424-68593.gif)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185417-94575.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185414-52099.gif)
椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185402-97078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185403-73866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185403-10982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185403-54388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185403-66470.png)
A.2 | B.4 | C.6 | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185355-71426.gif)
(1)若P到左焦点的距离为3,求到右准线的距离;
(2)如果F1为左焦点,F2为右焦点,并且
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185355-27444.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185356-15017.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185347-79907.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185347-77522.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185348-32787.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023185348-28997.jpg)
(1)求椭圆的方程.
(2)已知定点E(-1,0),若直线y=kx+2(k≠0)与椭圆交于C、D两点.问:是否存在k的值,使以CD为直径的圆过E点?请说明理由.
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