题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170141-84197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170141-13422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170141-75759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170142-18450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170142-54892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170142-52115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170142-80620.png)
(Ⅰ)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170141-84197.png)
(Ⅱ)设过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170142-52229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170141-84197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170143-56117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170143-70765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170143-35140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170143-78575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170143-47726.png)
(Ⅲ)试用
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170144-49704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170144-95378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170144-95378.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170144-10748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170144-12436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170145-47979.png)
(Ⅱ)设直线AB的方程为y=k(x-1)(k≠0),
代入
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170145-77694.png)
∵直线AB过椭圆的右焦点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170142-52229.png)
∴方程有两个不等实根.
记A(x1,y1),B(x2,y2),AB中点N(x0,y0),则x1+x1=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170145-93563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170145-88608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170144-12436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170145-29413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170146-41776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170146-93593.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170146-42309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170146-67679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170147-14186.png)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170147-17961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170147-13613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170147-66989.png)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170147-17961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170148-70599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170148-87810.png)
解析
核心考点
试题【(本小题满分12分)已知椭圆:的左、右焦点分别为离心率,点在且椭圆E上, (Ⅰ)求椭圆的方程; (Ⅱ)设过点且不与坐标轴垂直的直线交椭圆于两点,线段的垂直平分线】;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/20191023/20191023170133-95808.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170134-70703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170134-96105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170128-45272.jpg)
(I )求椭圆E的方程;
(II)垂直于OC的直线l与椭圆E交于A、B两点,当以AB为直径的圆P与y轴相切时,求直线l的方程和圆P的方程.
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170115-21268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170115-35064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170115-38902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170116-73950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170116-42065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170116-72365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170116-36786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170116-72365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170117-71880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170117-89961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170117-59398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170116-72365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170105-86310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170105-28527.png)
(1)求椭圆的标准方程;
2)若直线l过该椭圆的左焦点,交椭圆于M、N两点,且
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170106-49371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170051-19886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170051-95226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170051-73562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170051-89588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170052-52271.png)
A.30° | B.60° | C.120° | D.150° |
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