题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131805-84546.png)
(1)求抛物线D的方程;
(2)已知动直线l过点P(4,0),交抛物线D于A,B两点
(i)若直线l的斜率为1,求AB的长;
(ii)是否存在垂直于x轴的直线m被以AP为直径的圆M所截得的弦长恒为定值?如果存在,求出m的方程,如果不存在,说明理由。
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131805-44454.png)
(ii)存在直线m:x=3满足题意。
解析
(1)根据抛物线D的顶点是椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131805-84546.png)
(2)设A(x1,y1),B(x2,y2).(i)直线l的方程代入抛物线方程,利用韦达定理可求|AB|;
(3) 设存在直线m:x=a满足题意,则圆心M(
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131805-64028.png)
解:(1)y2=4x(3分)
(i)A(x1,y1) B(x2,y2) |AB|=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131805-44454.png)
(ii)设存在直线m:x=a,满足题意,则圆心M
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131805-99685.png)
当a=3时,弦长恒为定值2
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131805-32715.png)
核心考点
试题【(13分)已知抛物线D的顶点是椭圆的中心,焦点与该椭圆的右焦点重合。(1)求抛物线D的方程;(2)已知动直线l过点P(4,0),交抛物线D于A,B两点(i)若直】;主要考察你对抛物线的定义与方程等知识点的理解。[详细]
举一反三
如图,斜率为1的直线过抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131724-26279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131724-50107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131724-19534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131725-66702.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131725-38484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131725-66702.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131725-90900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131724-50107.png)
(Ⅰ) 若
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131726-23557.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131726-79155.png)
(Ⅲ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131726-39278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131726-16077.png)
已知直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131657-73854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131657-36867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131657-36867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131657-64843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131658-99403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131658-70151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131657-64843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131658-52649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131658-92068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131658-70151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131659-67753.png)
(1)求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131659-67753.png)
(2)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131659-35165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131659-67753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131659-80384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131659-35165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131659-35165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131604-41440.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131604-76741.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131604-76741.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131605-69722.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131605-64139.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131605-79789.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131605-27166.gif)
(1)求抛物线的方程.
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131606-48797.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131606-21057.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131536-58671.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131536-80485.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025131537-19085.gif)
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