Question

设原点坐标为O,抛物线y^2=4x与过焦点的直线交于A,B两点,求向量OA乘以向量OB等于多少

Answer 1

A(x1,y1),B(x2,y2),焦点(1,0) 直线:y=k(x-1) 向量OA乘以向量OB=x1x2+y1y2

联立 y=k(x-1) ,y^2=4x x^2-(2+4/k)x+1=0 x1x2=1 y1^2*y2^2=16 y1*y2=-4

向量OA乘以向量OB=x1x2+y1y2=-3