已知圆X2+Y2+8X-6Y+21=0与直线Y=MX交于P,Q两点,O为坐标原点,求向量OP乘OQ

已知圆X2+Y2+8X-6Y+21=0与直线Y=MX交于P,Q两点,O为坐标原点,求向量OP乘OQ
已知圆X2+Y2+8X-6Y+21=0与直线Y=MX交于P,Q两点,O为坐标原点,求向量OP乘OQ

已知圆X2+Y2+8X-6Y+21=0与直线Y=MX交于P,Q两点,O为坐标原点,求向量OP乘OQ
x^2+y^2+8x-6y+21=0
设p(x1,mx1) q(x2.mx2)
向量OP点乘OQ=x1x2+m^2x1x2= (m^2+1)x1x2
x1x2是方程x^2+m^2x^2+8x-6mx+21=0的两解
x1x2=21/(m^2+1)
向量 OP点乘OQ=x1x2+m^2x1x2=(m^2+1)x1x2=21