设点A(x1.x2),B(x2.y2)在抛物线y^2=2px(p>0)上，且OA垂直于OB
(1)求证:x1·x2＝４P^2;y1·y2=-4P^2;
(2)证明直线AB过定点（２P,0）;
(3)证明三角形AOB的面积的最小值为４P^2

y1^2 =2px1 ...(1), y2^2 =2px2 ...(2)
y1/x1 =2p/y1, y2/x2 =2p/y2
OA垂直于OB: (y1/x1)(y2/x2) =-1 =4p^2/(y1y2)
==> y1·y2 =-4p^2
(1)*(2): (y1y2)^2 =4p^2*(x1x2)
==> x1·x2 =4p^2

(y1-0)/(x1-2p) =(-4p^2/y2)/(4p^2/x2 -2p) =y2/(x2-2p)
==> 直线AB过定点(2p,0)

三角形AOB的面积 =(1/2)*OA*OB
= (1/2)根号[(x1^2+y1^2)(x2^2+y2^2)]
= (1/2)根号[(x1^2+2px1)(x2^2+2px2)]
= (1/2)根号{(x1x2)[x1x2+2p(x1+x2)+4p^2]}
= p*根号[2p(x1+x2)+8p^2]
>= p*根号[2p*2*根号(x1x2)+8p^2]
= 4p^2
==> 三角形AOB面积的最小值为4p^2