过抛物线y2=2px(p>0)的顶点O作两条互相垂直的弦交抛物线于A,B两点,求AB的中点M的轨迹方程

M(x,y)
xA+xB=2x,yA+yB=2y
(yA/xA)*(yB/xB)=-1
xA*xB=-yA*yB
(yA)^2*(yB)^2=2p*xA*2p*xB=4p^2*(-yA*yB)
yA*yB=-4p^2
(yA)^2+(yB)^2=2P(xA+xB)
(yA+yB)^2-2yA*yB=2p*2x
(2y)^2-2*(-4p^2)=4px
y^2-px+2p^2=0