题目
题型:不详难度:来源:
已知椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180019-28729.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180019-70973.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180019-39478.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180020-89312.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180020-73425.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180020-48696.gif)
(Ⅱ)若直线y=kx(k<0)与
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180020-48696.gif)
答案
|AF2|+|AB|+|BF2|=4a, ①
|AF2|+|BF2|=2|AB|, ②
|AF2|2+|AB|2=|
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180020-93994.gif)
由①、②、③,解得|AF2|=a,|AB|=a,|BF2|=a,
所以点A为短轴端点,b=c=a,Γ的离心率e==.…………………5分
(Ⅱ)由(Ⅰ),Γ的方程为x2+2y2=a2.
不妨设C(x1,y1)、D(x2,y2)(x1<x2),
则C、D坐标满足
由此得x1=-,x2=.
设C、D两点到直线AB:x-y+a=0的距离分别为d
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180021-32832.gif)
因C、D两点在直线AB的异侧,则
d1+d2=+=
===.………………………8分
∴S=|
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180021-52678.gif)
设t=1-k,则t>1,==,
当=,即k=-时,最大,进而S有最大值.……………………12分
解析
核心考点
试题【 (本题满分12分)已知椭圆的左、右焦点为,过点斜率为正数的直线交两点,且成等差数列。(Ⅰ)求的离心率;(Ⅱ)若直线y=kx(k<0)与交于C、D两点,求】;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
设椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175959-11042.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175959-36663.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175959-94629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175959-56855.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180000-69890.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180000-82206.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180000-35047.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180000-41436.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180001-27911.gif)
(I)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180001-92531.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175959-11042.gif)
(II)过
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180001-88467.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180001-26208.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180001-15827.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180002-78798.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180002-39394.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180003-65542.gif)
求四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180003-30219.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180004-83627.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175950-87057.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175950-12132.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175950-65072.gif)
(Ⅰ)求椭圆的方程;
(Ⅱ)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175950-89481.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175951-83948.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175951-48037.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175951-14712.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175951-36283.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175951-83948.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175937-64892.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-96737.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-41470.gif)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-51970.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-36841.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-51970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-16893.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175939-40989.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175939-31537.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175939-40808.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-51970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-36841.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175940-83943.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175940-45826.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175940-85038.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175939-40808.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-51970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175940-70266.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175917-29275.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175917-71376.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175917-15485.gif)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175917-74468.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175918-60104.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175917-74468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175918-63758.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175917-74468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175918-60104.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175918-56627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175918-86567.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175919-28119.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175919-18976.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175919-82481.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175911-32592.gif)
A.![]() | B.![]() |
C.![]() | D.![]() |
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