设P(x1,y1),Q(x2,y2)
联立两方程有(1+m^2)X^2+(8-6m)x+21=0(P,Q为直线与园的交点,两点的X坐标是方程的两解)
由韦达定理有x1+x2=(6m-8)/(1+m^2),x1*x2=21/(1+m^2),向量OP*向量OQ=(x1,y1)*(x2,y2)=x1*x2+y1*y2=x1*x2+m^2x1*x2=
(1+m^2)x1*x2=21
设P(x1,y1),Q(x2,y2)
联立两方程有(1+m^2)X^2+(8-6m)x+21=0(P,Q为直线与园的交点,两点的X坐标是方程的两解)
由韦达定理有x1+x2=(6m-8)/(1+m^2),x1*x2=21/(1+m^2),向量OP*向量OQ=(x1,y1)*(x2,y2)=x1*x2+y1*y2=x1*x2+m^2x1*x2=
(1+m^2)x1*x2=21