题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225336-34218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225336-84463.png)
(1)求椭圆的方程;
(2)设不过原点O的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225336-49924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225337-13506.png)
求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225337-39196.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225337-72597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225337-91976.png)
解析
试题分析:(1)先设出椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225337-48256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225336-34218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225338-84632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225336-49924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225338-89894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225338-16322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225338-99763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225339-80058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225337-13506.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225339-19834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225339-11709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225339-62500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225340-51792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225340-25793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225340-75804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225340-92255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225337-39196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225340-70806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225341-51354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225337-39196.png)
试题解析:(1) 由题意可设椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225337-48256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225341-85435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225341-31042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225341-74250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225342-43413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225342-57447.png)
所以椭圆的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225337-72597.png)
(2)由题意可知,直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225336-49924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225336-49924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225338-89894.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225338-16322.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225342-43492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225342-59036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225343-25139.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225343-86118.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225338-99763.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225343-83255.png)
因为直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225337-13506.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225343-99603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225339-19834.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225339-11709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225343-36042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225339-62500.png)
由于直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225340-25793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225340-51792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225340-75804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225340-92255.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225344-86761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225344-38799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225336-49924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225344-98640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225344-78737.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225345-77056.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225337-39196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225337-91976.png)
核心考点
试题【已知中心在原点O,焦点在x轴上,离心率为的椭圆过点(1)求椭圆的方程;(2)设不过原点O的直线与该椭圆交于P,Q两点,满足直线的斜率依次成等比数列,求面积的取值】;主要考察你对曲线与方程的应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225330-57993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225330-86132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225330-51621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225330-25234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225331-17039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225331-10597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225330-57993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225330-86132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225331-23216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225331-71150.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225315-36826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225316-33787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225316-86044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225316-51663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225316-11451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225317-17283.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225317-86786.png)
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225316-86044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225317-86786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225317-21504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225318-87174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225318-88850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225318-68200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225318-57998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225301-22386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225301-14995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225302-98665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225301-22386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225302-54357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225302-54357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225302-93683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225302-54357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225301-22386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225302-63918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225303-76414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225303-25528.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225301-22386.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225303-45204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225302-54357.png)
(3)设点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225303-76000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225301-22386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225302-63918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225303-76414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225304-73167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225304-97586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225304-48526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225305-12867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225305-56569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225255-41815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225255-99795.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225241-39959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225242-84732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225242-39897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225241-39959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225242-17404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225242-67163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225242-39897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225243-21450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225243-71084.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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