题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165746-79426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165746-77324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165746-73657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165746-72644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165746-21142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165746-85290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165747-27612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165747-95525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165747-16394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165747-52157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165747-94688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165747-75810.png)
(I)求椭圆的标准方程; (II)若点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165747-27612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165747-68306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165747-71131.png)
(III)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165748-29945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165748-74512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165748-47416.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165748-77342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165748-24123.png)
由椭圆的定义知,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165748-32453.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165748-74168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165748-92505.png)
所以所求椭圆的标准方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165749-61791.png)
(II)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165749-14228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165749-54228.png)
代入椭圆方程,得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165749-33167.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165750-87963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165750-66715.png)
代入直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165749-14228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165750-50066.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165747-71131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165750-61877.png)
(III)设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165750-66629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165751-29492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165751-39201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165751-40286.png)
直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165749-14228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165751-92137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165752-50344.png)
代入椭圆方程,消去
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165748-77342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165752-25576.png)
又因为点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165752-19749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165752-45869.png)
方程化简为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165752-31971.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165753-61907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165753-40558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165753-97781.png)
代入直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165749-14228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165753-30214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165753-11690.png)
同理
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165754-27726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165754-94726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165754-49107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165754-95068.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165755-18850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165755-71560.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165755-69237.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165755-11355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165755-33351.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165756-73465.png)
解析
核心考点
试题【已知椭圆两个焦点的坐标分别为,,并且经过点.过左焦点,斜率为的直线与椭圆交于,两点.设,延长,分别与椭圆交于两点.(I)求椭圆的标准方程; (II)若点,求点】;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/20191023/20191023165729-97638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165729-47364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165729-33542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165729-41743.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165717-35804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165717-94883.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165717-35804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165717-76612.png)
圆的焦点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165718-98641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165717-35804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165718-94191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165718-11794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165718-32647.png)
的取值范围为( )
A.![]() | B.![]() | C.![]() | D.![]() |
已知以原点为中心,F(
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165703-19470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165703-79576.png)
(1).求椭圆C的标准方程.
(2).设M、N为椭圆C上的两动点,且
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165703-24780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165703-79576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165703-48311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165704-91604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165651-88532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165651-38938.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165651-34688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165651-88532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165651-93046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165651-88423.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165651-88532.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165652-89251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165651-88532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165652-27728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165652-26831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165652-51874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165653-51890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165652-26831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165653-97784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165653-79795.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165653-66896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165644-71180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023165644-25918.png)
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