题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135208-25587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135208-80451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135208-25587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135208-95190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135208-10786.png)
(1)求椭圆的标准方程;
(2)设P为椭圆上一点,若过点M(2,0)的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-20349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-80677.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-15636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-26076.png)
解析
试题分析:
(1)抛物线的方程已知,则可以求出右焦点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135208-25587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-29458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-91180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-25382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-25382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-61784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135210-83700.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135210-63744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135210-39180.png)
(2)因为直线l与椭圆有交点,所以直线l的斜率一定存在,则设出直线l的斜率得到直线l的方程,联立直线l与椭圆方程得到AB两点横纵坐标之间的韦达定理,即
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135210-71275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-80677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135211-31960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135211-93865.png)
试题解析:
(1)设椭圆标准方程
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135211-15148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135211-92258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135211-34135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135212-58244.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-61784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135212-26500.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135212-94015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135212-50079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135212-49249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135213-27875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135213-98511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135213-77357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135213-83881.png)
所以椭圆的标准方程
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135214-56866.png)
(2)由题意,直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-20349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135209-20349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135214-92945.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135214-64332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135214-52056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135215-93731.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135215-74681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135215-32733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135215-99368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135215-90758.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135216-52192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135216-90548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135216-16141.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135216-13977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135216-74248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135217-69886.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135217-43157.png)
因为点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135217-45523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135217-91846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135218-37023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135218-50671.png)
再由①,得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135218-84105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135217-69886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135218-61159.png)
核心考点
试题【如图,椭圆的右焦点与抛物线的焦点重合,过且于x轴垂直的直线与椭圆交于S,T,与抛物线交于C,D两点,且(1)求椭圆的标准方程;(2)设P为椭圆上一点,若过点M(】;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/20191023/20191023135158-31531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135158-11966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135158-77146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135158-44383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135159-44790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135158-31531.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135147-73523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135148-33364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135148-32491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135148-82781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135148-80287.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135149-77694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135149-29316.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135134-69607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135135-43942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135135-22103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135135-98795.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135135-11407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135135-76184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135135-14862.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135134-69607.png)
(2)若动直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135135-92424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135136-50551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135134-69607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135136-24436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135136-63346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135136-80879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135136-67717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135136-64399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135137-48991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135123-41500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135123-18387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135123-44538.png)
(1)求椭圆C2的标准方程;
(2)设AB是过椭圆C2中心O的任意弦,l是线段AB的垂直平分线.M是l上的点(与O不重合).
①若MO=2OA,当点A在椭圆C2上运动时,求点M的轨迹方程;
②若M是l与椭圆C2的交点,求△AMB的面积的最小值.
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135109-55079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135110-85283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135110-74762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135110-76315.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135109-55079.png)
(2)设动直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135110-89599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135109-55079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135111-14065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135111-74280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135111-22322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135111-11880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135112-32904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135112-14950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135112-32904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023135112-32904.png)
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