题目
题型:不详难度:来源:
已知抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135826-30694.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135826-30773.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135826-38212.gif)
(1)若以弦
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135826-10162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135827-91202.gif)
(2)在(1)的条件下,若
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135827-20635.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135827-48561.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135827-91593.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135828-75253.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135828-47117.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135828-97634.gif)
以弦
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135826-10162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135828-89563.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135829-61084.gif)
②若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135829-70777.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135829-91102.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135829-91102.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135829-27447.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135830-95330.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135830-37435.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135830-39801.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135830-58250.gif)
以弦
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135826-10162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135830-15448.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135831-40518.gif)
又此时
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135831-55536.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135827-48561.gif)
<2>设动点R的坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135831-57363.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135831-83274.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135832-90103.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135832-71236.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135832-73567.gif)
①当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135832-56591.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135833-68594.gif)
②当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135833-29852.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135833-77285.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135833-89368.gif)
即得:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135834-58065.gif)
又因为点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135834-77447.gif)
所以由①②得R点的轨迹方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135827-91593.gif)
点评:此题也可设直线方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135834-80570.gif)
核心考点
试题【(本题满分13分)已知抛物线的焦点为F,直线过定点且与抛物线交于P,Q两点。(1)若以弦为直径的圆恒过原点,求p的值;(2)在(1)的条件下,若,求动点R的轨迹】;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
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135725-34834.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135725-89715.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135725-87989.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135725-99520.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135726-81966.gif)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135726-99314.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135726-20574.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135726-37514.gif)
(Ⅱ)记
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135727-14550.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135727-78214.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135727-69705.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135727-62998.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135728-30932.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135728-85242.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135728-44881.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135728-42844.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135729-50930.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135729-33167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135728-42844.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135716-66361.png)
A.p | B.2p | C.4p | D.不确定 |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135708-10717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135708-97285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135708-51915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135708-52755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135708-44567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135709-23872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135546-68439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025135546-50822.gif)
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