题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154209-43666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154210-27060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154210-90027.png)
(1)求椭圆的方程;
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154210-27040.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154210-42499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154211-78200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154211-48015.png)
解析
试题分析:(Ⅰ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154211-35328.png)
故所求椭圆为:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154211-27084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154210-90027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154212-18686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154212-64157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154210-42499.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154212-18534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154212-53338.png)
将直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154213-19254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154210-42499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154213-17899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154213-96306.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154213-84792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154213-97442.png)
又(-1,0)不在椭圆上,依题意有
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154214-15141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154214-35262.png)
由①②可得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154214-47792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154214-53338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154214-87476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154215-98945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154215-34921.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154215-89903.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154215-95740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154215-93408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154216-77129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154211-78200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154211-48015.png)
点评:直线与椭圆相交时常联立方程,利用韦达定理设而不求的方程转化求解出弦长,本题求解三角型面积最值转化成二次函数,有时利用均值不等式求最值,此题中第二小题属于难题
核心考点
试题【已知椭圆的离心率为,且过点(),(1)求椭圆的方程;(2)设直线与椭圆交于P,Q两点,且以PQ为对角线的菱形的一顶点为(-1,0),求:△OPQ面积的最大值及此】;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/20191023/20191023154204-17066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154205-81058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154205-73165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154205-65408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154205-59317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154150-22522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154150-29874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154150-66331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154150-22522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154150-29874.png)
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154150-22522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154150-29874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154152-51968.png)
2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154152-15828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154150-22522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154152-43848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154152-60567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154152-64636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154152-15828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154150-29874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154152-33444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154152-15828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154132-72578.png)
(1)求椭圆E的方程;
(2)设动直线L交椭圆E于A、B两点,且
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154132-50383.png)
已知椭圆的中心在原点,焦点在
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154120-20719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154120-64281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154120-24117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154121-61696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154121-33074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154121-78162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154121-61696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154121-11061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154121-65613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154121-20075.png)
(1)求椭圆方程;
(2)求证:对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154122-95522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154122-88592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154122-79367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154109-27031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154109-44214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154109-92328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154110-37224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023154110-48285.png)
A.![]() | B.![]() | C.![]() | D.![]() ![]() |
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