设△AOB的顶点均是在抛物线y^2=2px(p>0)上,其中O为坐标原点.若△AOB的垂心恰好是抛物线的焦点,求△AOB的面积.

△AOB的垂心恰好是抛物线的焦点,AB⊥X轴, OA=OB,xA=xB,yA=-yBp>0,F(P/2,0)设xA=xB=a,则y=±√(2pa)AF⊥OB设yA=√(2pa),yB=-√(2pa),则k(AF)*k(OB)=-1[√(2pa)/(a-p/2)]*[-√(2pa)/a]=-1a=5p/2AB=yA-yB=2√(2pa)=2p*...