题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221740-70727.png)
(1)求椭圆C的方程;
(2)过右焦点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221740-30320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221741-86041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221741-55177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221741-86041.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221741-35025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221741-60008.png)
解析
试题分析:(1)因为椭圆C:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221740-70727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221742-32077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221742-32077.png)
(2)因为过右焦点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221740-30320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221741-86041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221741-55177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221742-62036.png)
试题解析:(1)设椭圆C的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221742-90930.png)
由题意得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221742-70058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221741-35025.png)
(2)设直线的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221743-24651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221743-27794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221743-85111.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221743-89073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221743-68751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221744-51505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221744-58295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221744-79600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221745-12097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221745-32348.png)
由此得-
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221744-79600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221745-32348.png)
解方程得:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221745-42549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221745-26862.png)
代入-
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221744-79600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221745-32348.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221745-37819.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221746-42584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221746-85667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221746-55503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221741-60008.png)
核心考点
试题【已知椭圆C:的左、右焦点和短轴的一个端点构成边长为4的正三角形.(1)求椭圆C的方程;(2)过右焦点的直线与椭圆C相交于A、B两点,若,求直线的方程.】;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/20191025/20191025221734-16269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221734-35390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221734-88094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221735-85068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221735-67668.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221728-45794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221728-84056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221729-58419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221729-58419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221729-22198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221729-71146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221729-30699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221718-22503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221718-77211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221718-79713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221718-63010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221719-94815.jpg)
(1)求椭圆C的方程;
(2)求点P的坐标;
(3)设M是直角三角PAF的外接圆圆心,求椭圆C上的点到点M的距离
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221719-89410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221711-95662.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221700-57859.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221700-38619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221700-96943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221700-93207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221700-39460.png)
(1)求椭圆C的方程;
(2)若存在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221701-24266.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221701-17284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221701-16713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221701-23939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221700-93207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221702-16345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221702-43417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221702-56635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221702-66450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221700-93207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025221702-68863.png)
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