题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131054-83846.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131054-95795.gif)
(Ⅰ)求椭圆方程;
(Ⅱ)点M在椭圆上,求⊿MF1F2面积的最大值;
(Ⅲ)试探究椭圆上是否存在一点P,使
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131054-70279.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131055-34681.gif)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131055-21050.gif)
(Ⅲ)不存在,理由见解析。
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131055-97193.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131055-42146.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131055-80719.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131056-55919.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131056-39051.gif)
∴所求椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131055-34681.gif)
(Ⅱ)令
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131056-21969.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131056-55605.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131056-20998.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131057-40689.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131055-21050.gif)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131057-98464.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131057-63172.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131055-21050.gif)
(Ⅲ)假设存在一点P, 使
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131054-70279.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131057-70837.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131058-57887.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131058-58387.gif)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131058-13077.gif)
∴②2-①,得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131058-52464.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131059-19568.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131059-36314.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131059-36314.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131059-86903.gif)
∴不存在一点P, 使
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131054-70279.gif)
核心考点
试题【已知点是中心在原点,长轴在x轴上的椭圆的一个顶点,离心率为,椭圆的左右焦点分别为F1和F2 。(Ⅰ)求椭圆方程;(Ⅱ)点M在椭圆上,求⊿MF1F2面积的最大值;】;主要考察你对直线的倾斜角与斜率等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131041-30062.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131042-51884.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131042-89167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131042-20565.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131042-99941.gif)
(I)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131042-99941.gif)
(II)设椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131042-99941.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131043-78216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131043-93617.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131043-64799.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131043-78216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131043-60943.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131043-64799.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131043-53714.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131044-76123.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131043-60943.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131044-51381.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131044-51381.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131044-25929.gif)
(III)设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131044-25929.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131044-34701.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131045-42657.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131045-18059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131044-25929.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131045-49685.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131045-91115.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131028-99112.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022131028-14576.gif)
(2)证明:直线PQ与圆O相切.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022130958-99428.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022130958-28928.gif)
(Ⅰ)求抛物线C的焦点坐标和准线方程;
(Ⅱ)设直线AB上一点M,满足
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022130958-97187.gif)
(Ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022130958-60538.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022130958-54306.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022130949-96904.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022130949-41250.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022130949-99686.gif)
(1)求点P的坐标;
(2)设M是椭圆长轴AB上的一点,M到直线AP的距离等于
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022130950-81946.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022130950-28719.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022130950-52858.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022130942-78523.gif)
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