题目
题型:不详难度:来源:
已知椭圆C中心在原点,焦点在
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-27643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-76237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-54499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-80590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-27643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-47107.png)
(1)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-80590.png)
(2)求椭圆C长轴的取值范围。
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-49914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011041-96049.png)
解析
试题分析:解:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011041-52309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-80590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-76237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-54499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011041-37018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-80590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-49914.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-49914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011041-58067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011041-28073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-27643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011040-47107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011041-24730.png)
将
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011042-92240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011042-13131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011042-35232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011042-66181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011043-86601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011043-11261.png)
由①消去
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011043-45153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011043-27421.png)
③代入②得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011043-96514.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011044-26432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011044-58478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011044-26633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011044-63924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011041-37018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011041-96049.png)
点评:解决该试题的关键是能利用已知中的点和斜率来借助于点斜式方程表示出直线的方程,同时能结合直线与椭圆的相交,联立方程组,进而结合韦达定理和判别式来求解表示出长轴长,借助于参数a的范围得到所求,属于中档题。
核心考点
试题【(本小题满分12分) 已知椭圆C中心在原点,焦点在轴上,一条经过点且倾斜角余弦值为的直线交椭圆于A,B两点,交轴于M点,又.(1)求直线的方程;(2)求椭圆C长】;主要考察你对曲线与方程的应用等知识点的理解。[详细]
举一反三
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011028-13707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011028-58394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011028-56144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-40910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-22240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-93341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-79375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-64735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-16117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-13855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011030-65365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011030-96885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-13855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011030-97323.png)
(1)求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011029-13855.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011030-87599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011018-72960.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011014-85402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011014-72424.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011009-77139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011010-30412.png)
已知椭圆C的对称轴为坐标轴,且短轴长为4,离心率为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011001-91864.png)
(Ⅰ)求椭圆C的方程;
(Ⅱ)设椭圆C的焦点在y轴上,斜率为1的直线l与C相交于A,B两点,且
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026011001-83117.png)
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