Rt△AOB的三个顶点在抛物线y^2=2px(p>0)上，直角顶点O为原点，OA所在直线的方程为y=2x，

Rt△AOB,O(0,0),OA⊥OB,AB=5√3
OA:y=2x
k(OA)=2,k(OB)=-0.5,OB:y=-0.5x
yA^2=2p*xA......(1)
yA=2xA......(2)
(1)/(2):
yA=p,xA=0.5p

yB^2=2pxB......(3)
yB=-0.5xB......(4)
(3)/(4):
yB=-4p,xB=8p
(xA-xB)^2+(yA-yB)^2=AB^2
(0.5p-8p)^2+(p+4p)^2=(5√3)^2
p^2=12/13,p>0,p=√(12/13)=2√39/13
抛物线方程:y^2=(4√39/13)x