题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152157-51939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152157-59011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152157-48680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152157-24992.png)
证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152157-15245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152158-22363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152158-55969.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152158-33690.png)
解析
试题分析:(1)根据条件表示A、B两点,得到
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152158-59236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152158-90197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152157-24992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152158-46204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152158-90071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152158-23033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152157-24992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152159-10981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152159-37785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152159-62394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152159-11092.png)
试题解析:(1)解:依题意,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152159-65607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152159-31835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152159-10975.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152159-95933.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152159-71826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152200-29348.png)
所以 椭圆的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152200-69378.png)
(2)证明:由于
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152157-24992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152200-12049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152157-24992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152200-21752.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152158-33690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152200-89409.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152200-32481.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152200-51251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152200-75416.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-56003.png)
证法一:记△
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-93191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-34427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-94684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-18183.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-39673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-17047.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-64153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-63363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-66283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152202-54350.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152202-99568.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152202-56355.png)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152202-67384.png)
证法二:记△
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-93191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-34427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-94684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-18183.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-64153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152202-10549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152202-84141.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152202-99568.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152203-29778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152203-11641.png)
故线段
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152203-49749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152203-51614.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-39673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152201-17047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152203-12616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152203-51614.png)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152202-67384.png)
核心考点
试题【如图,A,B是椭圆的两个顶点, ,直线AB的斜率为.求椭圆的方程;(2)设直线平行于AB,与x,y轴分别交于点M、N,与椭圆相交于C、D,证明:的面积等于的面积】;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/20191023/20191023152134-52276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152135-31341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152135-68070.png)
(I)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152135-93187.png)
(II)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152136-91076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152135-93187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152136-43494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152136-95412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152136-49237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152136-14252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152136-46140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152137-35224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152121-24163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152121-17473.png)
(I)求椭圆C的方程;
(II)若直线y =kx交椭圆C于A,B两点,在直线l:x+y-3=0上存在点P,使得 ΔPAB为等边三角形,求k的值.
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152101-32426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152102-59583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152102-89879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152102-25059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152103-78815.png)
(I)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152103-23217.png)
(II)若点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152102-25059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152104-85265.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152104-34101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152103-23217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152104-24642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152104-91116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152105-18632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152102-25059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152105-49269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152105-12593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152105-87666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152051-85824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152051-22011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152051-56292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152034-14802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152034-84682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152035-94269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152035-16579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152035-28028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152035-11969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152035-28028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152037-24673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152037-17449.png)
(Ⅰ)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152035-28028.png)
(Ⅱ)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152037-72116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152035-28028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152037-31462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152038-52150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152038-58766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152038-35300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152037-72116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023152038-88272.png)
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