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

问题描述:

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

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...