题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045210-23303.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045211-69672.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045211-95070.gif)
(Ⅰ)求抛物线C的方程;
(Ⅱ)设A、B是抛物线C上两个动点,过A作平行于x轴的直线m,直线OB与直线m交于点N,若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045211-30789.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045211-20601.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045212-28470.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045212-58545.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045212-40003.gif)
过原点垂直于l的直线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045212-41285.gif)
解①②得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045213-54627.gif)
∵抛物线的顶点关于直线l的对称点在该抛物线的准线上.
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045213-39504.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045213-64739.gif)
∴抛物线C的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045211-20601.gif)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045213-69142.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045213-40575.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045214-10921.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045211-30789.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045214-72442.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045214-10400.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045214-57959.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045215-37673.gif)
直线ON:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045215-50693.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045215-54393.gif)
由③、④及
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045215-92967.gif)
点N的轨迹方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045212-28470.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045212-58545.gif)
核心考点
试题【已知以向量v=(1, )为方向向量的直线l过点(0, ),抛物线C:(p>0)的顶点关于直线l的对称点在该抛物线上.(Ⅰ)求抛物线C的方程;(Ⅱ)设A、B】;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/20191026/20191026045204-99151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045204-65224.gif)
过点M(0,m)且倾斜角为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045204-11865.gif)
A(x1,y1),B(x2,y2)两点,且
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045204-61009.gif)
(1)求m的值
(2)(文)若点M分
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045205-31451.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045205-34425.gif)
(理)若点M分
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045205-31451.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045205-37534.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045205-37534.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045205-61355.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045154-86376.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045154-92805.jpg)
点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045154-78053.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045154-46279.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045155-71548.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045155-58475.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045155-61212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045155-41357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045155-58475.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045155-93188.gif)
(I)证明: 点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045156-71072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045156-62249.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045156-71031.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045156-84079.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045154-92805.jpg)
(II)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045157-58431.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045141-38803.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045141-97119.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045142-18731.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045142-25944.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045142-40516.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045142-86900.gif)
(1)求圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045142-70535.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045143-95912.gif)
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045143-13067.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045142-70535.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045143-72035.gif)
|
|
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045143-69128.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045142-70535.gif)
过抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045129-96063.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045129-48538.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045129-83575.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045130-95245.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045130-77645.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045130-99404.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045130-62201.jpg)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045130-44395.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045130-12868.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045130-73413.gif)
(Ⅱ)记
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045130-64844.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045130-20537.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045130-91982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045131-68538.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045131-19230.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045131-17963.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045131-24601.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045131-57619.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045131-14094.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045131-42881.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045131-57619.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045123-39413.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045123-24328.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026045124-14064.gif)
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