过抛物线y^2=4px(p>0)的顶点作互相垂直的两弦OA.OB,求AB中点P的轨迹方程_数学解答

过抛物线y^2=4px(p>0)的顶点作互相垂直的两弦OA.OB,求AB中点P的轨迹方程

人气：485 ℃　时间：2019-08-21 13:36:06

解答

设A(pm^2,2pm),B(pn^2,2pn), ( m与n都不为0,且不相等) AB中点P(x,y)两弦OA.OB互相垂直得 (pmn)^2+4P^2mn=0mn=-4 (1)pm^2+pn^2=2x (2)pm+pn=y &nbs...