题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233516-95588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233516-89786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233516-95588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233517-41613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233517-47902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233516-95588.png)
(1)写出抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233516-95588.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233517-21241.png)
解析
试题分析:(1)椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233516-89786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233517-36061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233516-95588.png)
得抛物线的标准方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233517-21241.png)
(2)当直线AB的斜率不存在时,直线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233518-10061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233518-30855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233518-55379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233518-39038.png)
当直线AB的斜率存在时,设AB的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233519-62094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233519-28324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233519-85807.png)
消去
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233520-47156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233520-24586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233520-49444.png)
设A(
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233520-17368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233521-32016.png)
有
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233521-46848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233521-85248.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233522-26907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233522-82346.png)
综上所述,面积最小值为16 13分
点评:抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233522-32804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233522-78211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233523-70537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233523-92242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233523-50257.png)
当直线与圆锥曲线相交时,常联立方程借助于方程根与系数的关系求解
核心考点
试题【已知抛物线的焦点与椭圆的右焦点重合,抛物线的顶点在坐标原点,过点的直线与抛物线交于A,B两点,(1)写出抛物线的标准方程 (2)求⊿ABO的面积最小值】;主要考察你对曲线与方程的应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233502-16498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233503-75302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233503-73218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233503-70222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233504-21374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233504-46257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233504-52481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233505-84608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233502-16498.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233502-16498.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233504-52481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233505-72435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233505-43499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233505-66258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233503-70222.png)
(3)试问
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233505-43499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233505-84608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233504-52481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233458-48345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233458-20919.png)
①曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233458-48345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233459-79452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233458-48345.png)
③若曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233458-48345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233459-81886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233459-60848.png)
④若曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233458-48345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233500-53623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233500-99907.png)
其中所有正确命题的序号为__ _ __ .
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233448-88481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233448-97251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233448-54984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233449-36148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233449-69617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233449-30150.png)
(1)求椭圆C以及圆O的方程;
(2)当点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233449-48957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233450-13304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233438-24426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233439-10368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233439-84148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233439-13186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233439-87756.png)
A.![]() | B.![]() | C.![]() | D.![]() |
A.![]() | B.(0,![]() | C.![]() | D.(0,![]() |
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