OD⊥AB→k(OD)×k(AB)=-1→k(AB)=-2→AB:y=5-2x
与抛物线方程联立:y^2=(5-2x)^2=2px→4x^2-(20+2p)x+25=0
→xAxB=25/4,xA+xB=(10+p)/2
→yAyB=(5-2xA)(5-2xB)=25-10(xA+xB)+4xAxB=-5p
OA⊥OB→(xA,yA)×(xB,yB)=0→xAxB+yAyB=0=25/4-5p→p=5/4
→抛物线方程:y^2=5x/2
OD⊥AB→k(OD)×k(AB)=-1→k(AB)=-2→AB:y=5-2x
与抛物线方程联立:y^2=(5-2x)^2=2px→4x^2-(20+2p)x+25=0
→xAxB=25/4,xA+xB=(10+p)/2
→yAyB=(5-2xA)(5-2xB)=25-10(xA+xB)+4xAxB=-5p
OA⊥OB→(xA,yA)×(xB,yB)=0→xAxB+yAyB=0=25/4-5p→p=5/4
→抛物线方程:y^2=5x/2