题目
题型:不详难度:来源:
)椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181259-28537.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181259-10786.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181259-56453.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181259-22924.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181300-88164.gif)
(Ⅰ)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181259-28537.gif)
(Ⅱ)如图,过圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181300-17702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181300-13654.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181301-61715.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181259-28537.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181301-78409.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181301-46718.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181301-47442.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181301-15165.gif)
椭圆方程可设为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181302-33021.gif)
又,直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181259-22924.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181302-96446.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181302-29216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181303-34933.gif)
故椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181259-28537.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181303-20370.gif)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181303-34003.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181303-61510.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181304-85209.gif)
可见,另一条切线平行于
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181259-10786.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181301-46718.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181304-32059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181304-63904.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181304-54210.gif)
则其方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181305-84650.gif)
|
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181305-61183.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181305-92364.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181305-83489.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181302-29216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181306-65330.gif)
注意到直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181306-93063.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181306-69013.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181306-44668.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181307-21600.gif)
由于点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181301-61715.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181300-17702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181300-13654.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181307-69800.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181307-91122.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181301-46718.gif)
综上所述,过圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181300-17702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181301-61715.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181259-28537.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181306-69013.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181301-46718.gif)
解析
核心考点
试题【( (本题满分15分)椭圆的中心在原点,焦点在轴上,离心率为,并与直线相切.(Ⅰ)求椭圆的方程;(Ⅱ)如图,过圆:上任意一点作椭圆的两条切线. 求证:.】;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/20191023/20191023181249-26102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181250-53303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181250-93938.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181250-17495.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181250-53303.png)
且位于
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181250-84681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181251-24616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181251-47142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181251-92222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181251-59478.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181252-46626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181250-53303.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181244-57555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181240-18689.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181240-26233.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181240-64817.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181240-92695.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181240-37550.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181241-80762.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181232-63996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181232-56395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181232-70419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181232-81750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181233-84167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181233-65688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181233-15838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181233-98759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181234-76764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181234-48509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181224-98169.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181225-37112.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181225-77625.gif)
(1)求椭圆C的方程及离心率e;
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181224-98169.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023181225-87351.gif)
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