题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132627-77780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132627-34659.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132627-32101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132627-99800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132628-32088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132628-14414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132627-99800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132628-96372.png)
(1)求椭圆的离心率;
(2)若椭圆的焦点关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132628-34928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132629-41691.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132629-85376.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132629-52060.png)
解析
试题分析:(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132629-12146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132630-16033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132630-11760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132630-75476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132630-70236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132631-37660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132631-34527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132628-32088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132631-67521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132627-99800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132631-13822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132632-84628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132632-89786.png)
(2)由(1)的结论,设椭圆的一个焦点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132632-86222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132631-13822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132632-53164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132632-31053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132631-13822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132633-31498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132633-64060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132633-32657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132633-16260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132634-50979.png)
(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132634-98709.png)
设A、B两点的坐标分别为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132634-84041.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132634-75638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132635-30810.png)
∴M点的坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132635-83842.png)
又M点的直线l上:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132635-97726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132635-35225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132636-80214.png)
(2)由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132636-32654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132636-66917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132636-65591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132636-74715.png)
则有
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132637-69064.png)
由已知
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132637-71624.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132637-76476.png)
∴所求的椭圆的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132629-52060.png)
核心考点
试题【已知直线与椭圆相交于两点,点是线段上的一点,且点在直线上.(1)求椭圆的离心率;(2)若椭圆的焦点关于直线的对称点在单位圆上,求椭圆的方程.】;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/20191023/20191023132611-51614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132611-46386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132611-74047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132611-96881.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132611-83136.png)
(2)如图,过右焦点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132611-70831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132612-23230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132612-67927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132611-83136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132612-72987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132612-97304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132612-30593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132613-65154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132613-44745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132613-62779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132613-26560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132613-24931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132614-87254.png)
求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132614-40576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132614-90706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132555-60829.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132556-81208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132556-62457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132556-64631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132556-84754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132556-62457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132556-27663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132556-61669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132556-47832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132557-99125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132557-54182.png)
(1)求椭圆的标准方程;
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132557-51537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132557-11781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132557-95187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132556-62457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132556-84754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132557-36267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132557-94238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132558-72546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132558-15198.png)
已知直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132535-93191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132536-70621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132536-99683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132536-77618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132536-17413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132537-18743.png)
(1)求椭圆C的方程;
(2)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132535-93191.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132537-18123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132535-93191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132525-42321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132525-76374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132525-55510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132526-54806.png)
(1)求该椭圆方程;
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132526-57868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132526-97366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132526-53160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132526-48973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132526-24071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132527-67838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132506-75860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132506-64919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132507-40393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132507-39801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132507-31644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132507-36012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132508-90640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132508-98318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132508-78130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132508-13854.png)
(1)求椭圆C的方程;
(2)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132509-82936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132509-10291.png)
(3)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023132509-99195.png)
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