题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140133-29629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140133-97602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140134-12230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140134-72952.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140134-16661.png)
(2)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140134-39856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140135-75002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140135-65783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140135-84476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140135-17328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140135-86497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140134-16661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140136-81371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140136-47894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140136-46314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140136-13564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140137-89086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140137-39413.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140137-17047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140133-29629.png)
解析
试题分析:(1)利用待定系数法设椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140137-38814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140138-78742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140138-73237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140137-39413.png)
试题解析:(1)依题意,可设椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140138-89206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140137-38814.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140138-89786.png)
∵ 椭圆经过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140134-72952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140139-86252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140139-47775.png)
∴ 椭圆的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140137-17047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140139-72876.png)
(2)联立方程组
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140139-86846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140140-96671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140140-15289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140140-55573.png)
∵ 直线与椭圆有两个交点,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140140-86527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140141-34919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140141-53175.png)
∵ 原点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140141-88757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140141-97871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140138-78742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140138-73237.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140142-59837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140142-28613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140142-72874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140142-25621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140141-88757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140143-13090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140143-80202.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140143-12118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140143-84461.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140144-28096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140144-48433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140144-88025.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140144-17182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140145-77847.png)
综合①②可知:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140133-29629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140133-97602.png)
核心考点
试题【已知椭圆的焦点在轴上,离心率为,对称轴为坐标轴,且经过点.(1)求椭圆的方程;(2)直线与椭圆相交于、两点, 为原点,在、上分别存在异于点的点、,使得在以为直径】;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/20191023/20191023140122-71469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140122-36976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140123-49739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140123-43558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140123-31051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140123-98311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140123-12066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140123-49739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140123-63511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140123-79858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140124-51036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140123-63511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140123-79858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140124-82545.jpg)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140123-49739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140124-52748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140124-50715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140102-11877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140103-84937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140103-76141.png)
(1)求椭圆C的方程
(2)若过点M(2,0)的引斜率为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140103-68689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140103-72842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140104-95860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140104-52100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140104-68411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140050-60455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140050-95166.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140050-20544.png)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140050-22765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140050-19320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140051-23007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140051-86342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140038-64897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140038-48545.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140038-49040.png)
(1)求椭圆C的方程
(2)若过点M(2,0)的引斜率为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140039-84773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140039-10943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140039-75641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140039-30330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140015-74802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140015-33031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140016-17855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140015-74802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140016-14716.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140016-92212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140015-74802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140016-49213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140016-49213.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140015-74802.png)
(2)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140017-63751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140015-74802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140017-31588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140017-78069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140017-70264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140018-59921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023140018-48926.png)
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