题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163705-97487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163705-10381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163705-82614.png)
(1)求椭圆C的方程;
(2)设F是椭圆C的右焦点,M为椭圆上一点,以M为圆心,MF为半径作圆M。问点M满足什么条件时,圆M与y轴有两个交点?
(3)设圆M与y轴交于D、E两点,求点D、E距离的最大值。
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163705-42045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163706-77292.png)
(2) -4<x0<
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163706-94442.png)
(3)当x0=-
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163706-94442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163706-84727.png)
解析
解:(1)∵椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163706-13333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163706-13967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163705-10381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163705-82614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163707-44187.png)
∴椭圆C的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163705-42045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163706-77292.png)
(2)易求得F(1,0)。设M(x0,y0),则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163707-92806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163707-91127.png)
圆M的方程为(x-x0)2+(y-y0)2=(1-x0)2+y02,
令x=0,化简得y2-2y0y+2x0-1=0,⊿=4y02-4(2x0-1)2>0……①。
将y02=3(1-
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163707-92806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163706-94442.png)
(3)设D(0,y1),E(0,y2),其中y1<y2。由(2),得
DE= y2- y1=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163707-62185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163708-74174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163708-71248.png)
当x0=-
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163706-94442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163706-84727.png)
核心考点
试题【已知椭圆C: (a>b>0)的离心率为,且经过点P(1,)。(1)求椭圆C的方程;(2)设F是椭圆C的右焦点,M为椭圆上一点,以M为圆心,MF为半径作圆M。问点】;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/20191023/20191023163657-90408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163658-71437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163658-55816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163658-79101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163658-44899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163658-58309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163659-36245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163659-31241.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163642-13337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163642-91623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163643-37880.png)
(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163643-30622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163643-59375.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163643-37350.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163643-22954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163625-58951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163625-74411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163625-24226.png)
(1)求椭圆E的方程;
(2)是否存在圆心在原点的圆,使得该圆的任意一条切线与椭圆E恒有两个交点A,B,且OA
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163625-38670.png)
(3)设直线l与圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163626-47767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163617-49549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163618-85684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163618-76702.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163618-27103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163618-34688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163618-58357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163619-25832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163619-42639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163619-37559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163618-34688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163601-35153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163602-67596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163602-32183.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163602-21246.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163603-99905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023163603-24518.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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