题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001822-45341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001822-33894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001823-84064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001823-27794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001823-30108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001823-91101.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001823-55251.png)
(2)圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001824-14210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001824-93656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001824-14210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001824-39543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001824-14210.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001824-47891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001825-34173.png)
解析
试题分析:解:(1)依题意有:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001825-62802.png)
四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001823-30108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001823-55251.png)
可得:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001825-10948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001826-13172.png)
由①、②解得:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001826-38761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001823-55251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001824-47891.png)
(2)依题意得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001826-74939.png)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001826-28095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001827-52483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001827-58720.png)
圆心
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001824-14210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001827-52483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001824-14210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001824-39543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001827-16984.png)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001827-56343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001828-44539.png)
联立③、④得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001828-30148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001828-40937.png)
由此可得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001828-24946.png)
所以圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001824-14210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001825-34173.png)
点评:解决的关键是利用椭圆的几何性质来得到其方程,同时能借助于直线与圆的关系来得到圆的方程,属于基础题。
核心考点
试题【己知椭圆的离心率为,是椭圆的左右顶点,是椭圆的上下顶点,四边形的面积为.(1)求椭圆的方程;(2)圆过两点.当圆心与原点的距离最小时,求圆的方程.】;主要考察你对曲线与方程的应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001817-63758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001817-18092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001818-53348.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001818-10073.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001805-35267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001805-49452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001805-13215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001805-81912.jpg)
(1)求椭圆C的方程;
(2)过点M
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001805-83163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001757-98890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001757-56644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001757-39040.png)
(1)判断点P与直线l的位置关系,说明理由;
(2)设直线l与直线C的两个交点为A、B,求
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001758-82097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001744-78806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001744-70328.png)
(Ⅰ)求椭圆C的方程;
(Ⅱ)过点P(0,2)分别作直线PA,PB交椭圆C于A,B两点,设直线PA,PB的斜率分别为k1,k2,
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001744-87445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001737-57557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001738-72283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026001738-55571.png)
则它的离心率为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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