题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195549-39209.gif)
设椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-25982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-37548.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-58765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-69258.gif)
(1) 若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-58765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-25982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-25982.gif)
(2) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195551-50430.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195551-77751.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-25982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-58765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195551-32860.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195551-71842.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195552-27129.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195552-94290.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-58765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-25982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-58765.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195552-26406.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195552-87963.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195553-79762.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195553-78313.gif)
解:(1)因为抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-58765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-25982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195553-21193.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195553-90382.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195554-22606.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-25982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195552-26406.gif)
(2)由题设可知
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195554-70320.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195551-32860.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195554-70297.gif)
则由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195551-71842.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195554-58944.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195554-42595.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195555-33643.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195555-46206.gif)
由于点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195555-67827.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-58765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195555-21785.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195555-46206.gif)
②式代入①式并化简得:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195556-83032.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195556-64143.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195556-77073.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195556-49951.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195556-23294.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195552-94290.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195557-16283.gif)
因为重心在
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-58765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195557-65934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195557-50842.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195557-65049.gif)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195554-70320.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-25982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195558-35192.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195558-91273.gif)
所以椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-25982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195552-87963.gif)
抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195550-58765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195553-79762.gif)
核心考点
试题【设椭圆:,抛物线:.(1) 若经过的两个焦点,求的离心率;(2) 设,又为与不在轴上的两个交点,若的垂心为,且的重心在上,求椭圆和抛物线的方程.】;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
(I) 求考察区域边界曲线的方程:
(II) 如图4所示,设线段
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195543-80622.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195543-92752.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195536-33585.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195536-10677.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195536-25724.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195537-45887.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195537-95802.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195537-70103.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195538-33003.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195538-77333.gif)
A.1 | B.![]() | C.![]() | D.2 |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195528-60357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195528-97816.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195528-58459.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195529-79464.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195529-72301.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195529-29754.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195530-27803.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195525-64862.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195520-33050.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195520-43242.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023195520-68228.gif)
的面积为_____________________。
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