Question

已知圆 X的平方+Y的平方+8X-6Y+21=0与直线Y=MX交于点P、Q两点,O为坐标原点,求证：OP×OQ为定值

Answer 1

y=mx代入方程X的平方+Y的平方+8X-6Y+21=0

x^2+m^2x^2+8x-6mx+21=0

(1+m^2)x^2+(8-6m)x+21=0

x1x2=21/(1+m^2)

P(x1,mx1)Q(x2,mx2)

|OP|=√(1+m^2)|x1|

|OQ|=√(1+m^2)|x2|

|OP||OQ|=(1+m^2)|x1x2|=21