题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170425-65534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170425-12079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170425-59937.png)
(Ⅰ)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170425-65534.png)
(Ⅱ)若过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170425-67414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170426-13420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170425-65534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170426-27117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170426-41709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170426-86557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170425-65534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170426-13420.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170426-57510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170427-37582.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170427-11097.png)
(Ⅱ)当直线l与x轴垂直时,A,B分别为椭圆短轴的两端点,显然以A,B为直径的圆不过椭圆C的右顶点,故直线l与x轴不垂直
设直线l的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170427-58038.png)
则由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170428-65250.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170428-89039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170428-35764.png)
因为以AB为直径的圆过椭圆C的右顶点D(2,0),
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170428-30766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170429-82742.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170429-36614.png)
当k=1时,直线l过椭圆右顶点(2,0),不合题意,
所以k=7,故直线l的方程是
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170429-52792.png)
解析
核心考点
试题【已知椭圆的中心在坐标原点,焦点在轴上,离心率为,椭圆的短轴端点和焦点所组成的四边形周长等于8。(Ⅰ)求椭圆的方程;(Ⅱ)若过点的直线与椭圆相交于两点(不是左右顶】;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/20191023/20191023170409-68165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170409-13037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170409-68165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170409-66793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170409-61268.jpg)
(Ⅰ)求椭圆的方程;
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170409-22750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170358-52256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170358-69167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170359-70654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170359-67751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170359-49252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170359-65976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170342-61217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170342-56136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170342-92202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170342-40688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170342-82272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170342-88214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170343-50314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170343-38889.png)
(1)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170342-88214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170343-53660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170343-83285.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170343-54715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170342-88214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170343-55082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170343-90660.png)
(3)在
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170343-53660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170343-30742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170344-60771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170344-52425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170343-30742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170334-71411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170334-62345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170334-48392.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170326-93777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170326-52474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170326-18602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170326-40350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170327-84494.png)
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