题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200235-79920.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200236-79806.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200236-90588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200236-88249.gif)
(I)是否存在
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200237-40922.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200237-15721.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200237-80470.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200237-40922.gif)
(II)若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200237-90501.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200237-40922.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200238-10509.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200237-80470.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200238-49188.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200238-32780.gif)
直线AB:y=k(x-m),
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200238-54428.gif)
设A(x1, y1)、B(x2,y2),则x1+x2=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200239-93854.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200239-31769.gif)
则xm=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200239-36318.gif)
若存在
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200239-77665.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200240-43962.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200240-38158.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200240-85362.gif)
即N点坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200241-88035.gif)
由N点在椭圆上,则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200241-57970.gif)
即5k4-2k2-3=0.∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200241-99003.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200241-87769.gif)
故存在
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200238-10509.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200237-80470.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200242-31091.gif)
=(1+k2)x1x2-k2m(x1+x2)+k2m2
=(1+k2)·
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200242-67483.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200242-47930.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200242-43754.gif)
即k2-15≤-20k2-12,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200243-44845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200238-49188.gif)
核心考点
试题【如图,已知椭圆C:,经过椭圆的右焦点F且斜率为的直线l交椭圆C于A、B两点,M为线段AB的中点,设O为椭圆的中心,射线OM交椭圆于N点.(I)是否存在,使对任意】;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/20191023/20191023200223-39620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-23516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-90547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-97314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-67949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-78039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-81079.png)
(Ⅰ)当⊙
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-36850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-34073.png)
(Ⅱ)当⊙
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-92137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
(Ⅲ)求证:⊙
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200224-48351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200207-27260.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200207-73638.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200207-12934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200208-89410.gif)
(Ⅰ)求动圆圆心的轨迹C;
(Ⅱ)若轨迹C与直线y="kx+m" (k≠0)相交于不同的两点M、N,当点A(0,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200208-75942.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200208-73263.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200209-99432.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200202-18351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200202-98542.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200202-36378.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200203-89648.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200203-60620.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200203-67210.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200204-23740.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200148-12735.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200148-69881.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200148-50112.gif)
(1)求椭圆的方程;
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200149-90304.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200149-13568.gif)
已知椭圆C的中心在原点、焦点在
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200138-30832.gif)
(Ⅰ)求椭圆C的标准方程;
(Ⅱ)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200138-92805.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200139-99114.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200139-69809.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023200138-92805.gif)
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