性质1如图1,抛物线E:y2=2px(p0)的焦点为F,过焦点F作两条互相垂直的弦AB,CD,设弦AB,CD的中点分别为M,N,则线段MN恒过定点T((3p)/2,0),且以AB,CD为直径的两圆公共弦中点的轨迹是以OT为直径的圆.证明设AB的方程为:x=ty+2p,代入y2=2px,并整理得y2-2pty-p2=0.设A(x1,y1),B(x2,y2), Properties 1 As shown in Figure 1, the parabola E: y2 = 2px (p0) has the focus F, and the focus F makes two chords AB, CD perpendicular to each other. The middle points of the strings AB and CD are respectively M and N, MN constant over a fixed point T ((3p) / 2,0), and AB, CD as the diameter of the two circular public centers of the midpoint of the trajectory is OT diameter circle prove AB set equation is: x = ty + 2p, into y2 = 2px, and finishing y2-2pty-p2 = 0. Let A (x1, y1), B (x2, y2),