设A(x1,y1),B(x2,y2)是抛物线y2=2px(p>0)上两点,且满足OA⊥OB,则y1y2等于_.

问题描述:

设A(x1,y1),B(x2,y2)是抛物线y2=2px(p>0)上两点,且满足OA⊥OB,则y1y2等于______.

∵A(x1,y1),B(x2,y2)是抛物线y2=2px(p>0)上的两点,并且满足OA⊥OB.
∴kOA•kOB=-1,∴x1x2+y1y2=0,∴

(y1y2)2
4p2
+y1y2=0,
则y1y2=-4p2
故答案为:-4p2