题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131221-45286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131221-61338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131222-81908.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131222-88992.png)
(1)求椭圆C的标准方程;
(2)设O为坐标原点,T为直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131222-49372.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131222-63714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131222-35694.png)
解析
试题分析:(1)由已知得:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131222-68441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131222-29399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-90775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-57199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-11490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-82797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-68717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-18533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-78195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-17474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-86024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-13877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131224-59614.png)
再结合韦达定理即可得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-86024.png)
试题解析:(1)由已知得:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131222-68441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131222-29399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-90775.png)
又由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-57199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131224-14137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131222-63714.png)
(2)椭圆方程化为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-82797.png)
设T点的坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131224-68197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131224-63225.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131224-73456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131224-80813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-68717.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131225-11859.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131225-21985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-68717.png)
将
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-68717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-18533.png)
其判别式
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131225-80530.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131225-37207.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131225-10227.png)
因为四边形OPTQ是平行四边形,所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131223-13877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131224-59614.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131225-54431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131226-72494.png)
此时四边形OPTQ的面积
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131226-61565.png)
【考点定位】1、直线及椭圆的方程;2、直线与圆锥曲线的位置关系;3、三角形的面积.
核心考点
试题【已知椭圆C:()的左焦点为,离心率为.(1)求椭圆C的标准方程;(2)设O为坐标原点,T为直线上任意一点,过F作TF的垂线交椭圆C于点P,Q.当四边形OPTQ是】;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/20191023/20191023131203-61861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131204-58486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131204-76973.png)
(1)若椭圆C上一动点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131204-96768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131204-30333.png)
(2)在(1)的条件下,过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131204-67900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131204-56486.png)
(3)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131204-85766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131204-25900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131204-52638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131153-90800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131154-71383.png)
A.![]() | B.![]() | C.![]() ![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131144-74414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131144-36088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131144-61847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131144-58552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131145-87910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131145-49378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131145-57256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131146-14991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131146-48724.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131145-49378.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131146-35356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131139-52752.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131139-65878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131139-68034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131140-55830.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131140-33448.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131128-10291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131128-64305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131128-92720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131128-52704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131128-75974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131129-39178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131129-35438.png)
(1)求椭圆的方程;
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131129-88965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131129-10079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131129-37550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131129-84173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023131129-10079.png)
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