题目
题型:不详难度:来源:
如图,抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155816-15544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155816-42523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155816-50794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155817-83199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155817-12606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155817-15668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155817-76892.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155817-49942.png)
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155818-89588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155818-49825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155818-36742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155818-81232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155819-18626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155817-49942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155819-71019.png)
(I)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155819-78696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155819-32846.png)
(II)记
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155819-94164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155820-97554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155818-49825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155820-43332.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155820-26436.png)
(2) (I)见解析;(II) 不存在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155818-49825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155820-43332.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155820-40973.png)
(2)(I) 证明
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155819-78696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155819-32846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155821-34618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155821-39153.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155821-53312.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155821-33932.png)
解;(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155821-80103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155822-81842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155822-16326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155822-42535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155822-74293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155817-49942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155820-26436.png)
(2)(I)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155818-49825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155822-70800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155823-48079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155823-16816.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155823-21594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155823-31279.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155823-19423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155819-78696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155819-32846.png)
(II)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155824-27262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155824-98171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155824-59365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155822-74293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155824-98171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155824-16850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155824-47996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155825-86108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155825-88083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155825-56622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155822-74293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155818-49825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155820-43332.png)
核心考点
试题【(本小题12分)如图,抛物线的焦点到准线的距离与椭圆的长半轴相等,设椭圆的右顶点为在第一象限的交点为为坐标原点,且的面积为(1)求椭圆的标准方程;(2)过点作直】;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
已知椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155804-58911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155804-77782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155804-51245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155804-70460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155805-71664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155805-21696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155804-51245.png)
(1)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155804-51245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155805-83833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155805-81590.png)
(2)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155806-82727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155806-56514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155753-70423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155753-44038.png)
(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155754-21959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155753-70423.png)
(2)点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155754-74282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155753-70423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155754-38638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155748-59709.png)
∥AB(O为原点), 则该椭圆的离心率是 ( )
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155748-15991.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155743-48435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155744-97195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155744-13910.png)
(I)求椭圆的方程;
(II)直线l(与坐标轴不平行)与椭圆交于不同的两点A、B,且线段AB中点的横坐标
为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155744-47798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155737-78949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023155738-13095.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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