Question

已知抛物线y=4x,直线l过抛物线有2个交点A和B,已知向量OA与向量OB的乘积为-4,求证该直线l过一定点,

Answer 1

y=4/x

y=kx+b

交点A(x1,y1) B(x2,y2)

OA.OB=x1x2+y1y2=-4

y1=4/x1

y2=4/x2

y1y2=16/(x1x2)

-4-x1x2=16/(x1x2) x1x2=t

t^2+4t+16=0

deta=16-64