题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152820-89742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152820-22658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152821-25133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152821-83770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152821-79163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152821-75663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152820-89742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152822-73101.png)
(Ⅰ)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152820-89742.png)
(Ⅱ)点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152822-53989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152820-89742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152822-98819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152822-72177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152822-98459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152820-89742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152823-32005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152823-82627.png)
(Ⅲ)在(Ⅱ)的条件下,过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152822-53989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152823-37437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152823-69645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152823-69645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152820-89742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152822-98819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152824-80920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152824-40152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152824-29970.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152824-24056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152825-32993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152825-86482.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152825-42692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152821-79163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152821-75663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152825-74422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152826-80881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152826-46434.png)
所以椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152820-89742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152826-58645.png)
(Ⅱ)由(Ⅰ)知
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152826-31287.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152827-37388.png)
由椭圆定义得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152827-19436.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152822-98459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152822-72177.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152827-11424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152827-34017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152828-99178.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152828-24083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152828-49150.png)
另解:由题意可知:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152828-82949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152829-93246.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152829-24814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152829-56050.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152829-47236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152829-23633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152830-28228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152829-23633.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152830-45695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152830-45639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152830-10855.png)
(Ⅲ)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152823-69645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152820-89742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152822-53989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152830-73133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152831-15284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152831-81776.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152831-13285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152824-24056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152831-35254.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152832-95832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152832-36278.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152832-21737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152832-38525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152833-10701.png)
另解:由题意可知,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152823-69645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152822-53989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152833-92618.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152833-74959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152833-59346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152824-29970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152834-23905.png)
【考点定位】本题通过椭圆的离心率、焦点、弦长、定义等基本知识来考查运算能力、推理论证能力。第一问较为简单,通过
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152834-12348.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152824-24056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152823-32005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152822-98819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152823-82627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152823-69645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152834-68782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152834-25330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152834-36365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152835-67961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152832-36278.png)
核心考点
试题【椭圆: 的左、右焦点分别是,离心率为,过且垂直于轴的直线被椭圆截得的线段长为。(Ⅰ)求椭圆的方程;(Ⅱ)点是椭圆上除长轴端点外的任一点,连接,设的角平分线交的长】;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/20191023/20191023152754-89410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152758-34474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152758-29094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152758-46402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152759-95396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152759-84945.png)
(I)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152758-34474.png)
(II)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152759-94815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152758-34474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152759-39315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152800-53715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152800-91462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152801-77666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152801-31634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152758-34474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152801-95819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152801-54544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152801-59968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152734-27579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152734-27579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152734-87269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152734-49053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152734-27579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152653-47127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152653-89826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152653-53445.png)
(Ⅰ) 求椭圆的方程;
(Ⅱ) 设A, B分别为椭圆的左右顶点, 过点F且斜率为k的直线与椭圆交于C, D两点. 若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152654-67012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152649-47061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152649-42149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152649-27814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152649-76804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152649-46585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152650-85038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152649-76804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152650-25352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152650-77423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152650-44396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152631-26929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152631-89124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152631-61180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152631-15018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152632-31706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152632-33283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152632-58401.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152632-99903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152633-23429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152633-75652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152633-37054.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152633-37054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152633-36969.png)
(3)直接写出
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152633-37054.png)
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