题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170301-58239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170301-23945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170301-96948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170301-20666.png)
(1)求抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170301-39677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170302-92641.png)
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170301-23945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170301-39677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170302-85780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170302-63800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170302-24327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170302-64844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170302-89688.png)
答案
解:(Ⅰ)由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170301-58239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170302-21355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170301-20666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170303-73955.png)
所以抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170301-39677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170303-10065.png)
同理由椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170301-96948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170303-80997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170303-24301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170301-20666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170303-43057.png)
得椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170302-92641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170304-93075.png)
总之,抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170301-39677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170303-10065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170302-92641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170304-93075.png)
(Ⅱ)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170304-39237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170304-34926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170304-76677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170304-25115.png)
联立方程组
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170304-86058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170302-24327.png)
得:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170305-77636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170305-66028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170305-16201.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170305-32044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170305-75331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170306-71899.png)
整理得,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170306-78629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170306-17493.png)
解析
核心考点
试题【. (本小题满分12分)已知抛物线的焦点以及椭圆的上、下焦点及左、右顶点均在圆上.(1)求抛物线和椭圆的标准方程;(2)过点的直线交抛物线于、两不同点,交轴于点】;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/20191023/20191023170251-51427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170251-20176.png)
线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170251-93102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170252-19712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170252-16153.png)
(I)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170252-51953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170252-49336.png)
(II)求满足
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170253-71781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170253-80934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170246-94687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170246-59359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170246-94925.png)
A.![]() ![]() | B.![]() | C.![]() | D.![]() ![]() |
已知椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170230-65735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170230-34170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170230-34012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170231-32312.png)
点。
(Ⅰ)求椭圆标准方程;
(Ⅱ)设动点P满足:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170231-90140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170231-45544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170231-70555.png)
使得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170231-13414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170231-70555.png)
(Ⅲ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170231-82350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170231-64962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170231-82350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170231-44990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170231-62584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170231-43853.png)
交椭圆于点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170232-66964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170232-60148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170221-96261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170221-25304.png)
的焦点,若∠AFB=
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170221-88474.png)
A、
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170222-76881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170222-67533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170222-44592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170222-47646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023170213-53824.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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