题目
题型:不详难度:来源:
已知椭圆的一个顶点为(-2,0),焦点在x轴上,且离心率为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183057-29218.gif)
(1)求椭圆的标准方程.
(2)斜率为1的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183057-23325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183057-23325.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183057-65628.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183058-56530.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183058-13907.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183058-45456.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183058-64187.gif)
(2)将直线l:y=x+b代入椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183058-64187.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183059-45751.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183059-53402.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183059-54118.gif)
由韦达定理得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183059-38721.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183100-87180.gif)
又点O到直线l的距离
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183100-57639.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183100-47641.gif)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183100-42736.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183059-54118.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183101-60937.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183101-47416.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183101-82846.gif)
∴所求的直线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183101-29725.gif)
解析
核心考点
试题【 (本小题12分)已知椭圆的一个顶点为(-2,0),焦点在x轴上,且离心率为.(1)求椭圆的标准方程.(2)斜率为1的直线与椭圆交于A、B两点,O为原点,当△A】;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/20191023/20191023183053-16703.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183053-27330.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183054-72456.gif)
已知椭圆的一个顶点为(-2,0),焦点在x轴上,且离心率为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183046-70906.gif)
(1)求椭圆的标准方程.
(2)斜率为1的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183046-75643.gif)
当△AOB的面积最大时,求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183046-75643.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183040-60234.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183040-95773.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183041-79772.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183041-22751.jpg)
A.![]() | B.![]() | C.![]() | D.![]() |
如图,椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183022-21998.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183022-80318.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183022-64399.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183022-86890.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183022-64399.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183022-49161.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183022-73008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183023-64403.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183023-26479.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183023-45407.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183022-64399.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183022-49161.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183023-45407.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183022-64399.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183023-68239.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183023-45407.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183023-20284.gif)
(Ⅱ)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183023-95216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183024-44851.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183024-16387.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183024-16387.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183023-20284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183024-23093.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183024-68023.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183025-48707.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183024-16387.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183012-57971.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183012-74585.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183012-62541.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183013-83437.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183013-76172.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183013-55279.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183013-88480.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183014-40720.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183014-91429.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183014-29181.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183014-46697.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183015-87054.jpg)
⑴求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183012-57971.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183014-29181.gif)
⑵若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183015-44662.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183013-76172.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183015-25094.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183015-44662.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183015-77914.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183014-29181.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183016-20152.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183016-87204.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183015-44662.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183013-76172.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023183015-77914.gif)
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