题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183136-64589.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183136-79340.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183136-63766.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183137-26868.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183137-44998.gif)
(1)、求椭圆C的方程及其“伴椭圆”的方程;
(2)、若倾斜角为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183137-45298.gif)
(3)、若点P是椭圆C“伴椭圆”上一动点,过点P作直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183137-32035.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183137-32035.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183137-82133.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183138-40793.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183138-58149.gif)
所以椭圆的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183138-65054.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183138-56563.gif)
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183138-98505.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183139-30970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183139-66899.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183139-92744.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183139-47467.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183139-67009.gif)
圆心到直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183138-98505.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-68439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-53413.gif)
(3)①、当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-25641.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-11764.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-11764.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-27022.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-39077.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-11764.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-27022.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-11764.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183141-85365.gif)
此时经过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183141-50718.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183141-70130.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183141-39363.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183142-60357.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183142-54082.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183141-39363.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183142-60357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-25641.gif)
同理可证
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-11764.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-39077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-25641.gif)
②、当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-25641.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183142-39795.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183142-24947.gif)
设经过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183142-39795.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183143-33422.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183143-93562.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183143-41815.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183143-68420.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183143-38861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183144-63850.gif)
经过化简得到:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183144-50554.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183142-24947.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183144-69654.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-25641.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183144-21999.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-25641.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183144-21999.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183144-69654.gif)
因而
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183144-15609.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183140-25641.gif)
解析
核心考点
试题【给定椭圆C:,称圆心在原点O、半径为的圆是椭圆C的“伴椭圆” ,若椭圆C的一个焦点为,其短轴上的一个端点到距离为;(1)、求椭圆C的方程及其“伴椭圆”的方程;(】;主要考察你对椭圆的定义与方程等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183129-78673.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183129-84501.gif)
A.![]() | B.![]() | C.2 | D.1 |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183124-44154.gif)
弦长为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183124-16359.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183120-57612.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183120-55393.gif)
已知椭圆C的中心在原点,焦点在x轴上,左右焦点分别为F1,F2;且
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183110-41269.gif)
点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183110-38142.gif)
(1)求椭圆C的方程;
(2)过F1的直线l与椭圆C相交于A、B两点,且△AF2B的面积为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183110-90884.gif)
心且与直线l相切的圆的方程.
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183105-41437.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183105-38135.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183106-40030.gif)
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