题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-17701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-86703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-61530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-68223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-14833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-55711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-14785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-55711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-14785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-92627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-56575.png)
(1)求椭圆的标准方程;
(2)求四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-58734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144640-66030.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144640-23652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144640-35632.png)
解析
试题分析:(1)由离心率为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-86703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144640-40041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144641-53361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144641-14548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144640-23652.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-55711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-14785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-55711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-14785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-55711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-14785.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-55711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-14785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144641-93566.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-55711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-14785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-55711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144641-66666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-14785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144641-41649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-90203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-55711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-64544.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-96588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-25354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144643-67175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144643-10520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144643-73987.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144643-44501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144644-79241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-90203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144644-36148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-90203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144644-97743.png)
(2),注意到方程(1)的结构特征,或图形的对称性,可以用
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144641-41649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144641-66666.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144644-98384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-90203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144645-43850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144645-84447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-90203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144645-59915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-90203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144645-12073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-58734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144640-35632.png)
试题解析:(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144640-40041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144641-53361.png)
将点P的坐标代入椭圆方程得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144641-14548.png)
故所求椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144640-23652.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-55711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-14785.png)
此时四边形的面积为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144641-93566.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-55711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-14785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-55711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144641-66666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-14785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144641-41649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-90203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144638-55711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-64544.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-96588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-25354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144643-67175.png)
消去
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144643-10520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144643-73987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-90203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144643-44501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144644-79241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-90203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144644-36148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-90203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144644-97743.png)
注意到方程(1)的结构特征,或图形的对称性,可以用
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144641-41649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144641-66666.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144644-98384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-90203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144646-89281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144645-84447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-90203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144646-15626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144642-90203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144645-12073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144639-58734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144640-35632.png)
核心考点
试题【已知椭圆的离心率为,且经过点. 过它的两个焦点,分别作直线与,交椭圆于A、B两点,交椭圆于C、D两点,且.(1)求椭圆的标准方程;(2)求四边形的面积的取值范围】;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/20191023/20191023144620-39039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144620-11664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144621-36754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144621-73367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144621-74465.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144620-39039.png)
(2)设过点P(-2,0)的直线与椭圆E交于A、B两点,且满足
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144621-86552.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144622-30143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144622-27685.png)
②若M、N分别为椭圆E的左、右顶点,证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144622-50733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144606-59240.png)
A.![]() | B.![]() | C.![]() | D.4 |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144542-80378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144543-45561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144543-76068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144543-38724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144543-97519.png)
(1)求椭圆C的方程:
(2)设椭圆的左、右顶点为A,B,过
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144543-95409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144543-23369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144543-86953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144518-71727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144518-83936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144518-92742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144518-65026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144518-94868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144519-42320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144519-93847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144519-45671.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144518-83936.png)
(2)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144519-31955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144518-83936.png)
点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144519-41562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144519-15320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144519-11495.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144519-74181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144519-46171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023144506-60053.png)
A.2 | B.4 | C.6 | D.5 |
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