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与向量OQ的积的值快.向量
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![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与向量OQ的积的值快.向量](/uploads/image/z/3706746-42-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%9C%86x2%2By2%2B8x-6y%2B21%3D0%E4%B8%8E%E7%9B%B4%E7%BA%BFy%3Dmx%E4%BA%A4%E4%BA%8EP+Q%E4%B8%A4%E7%82%B9.O%E4%B8%BA%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9%2C%E6%B1%82%E5%90%91%E9%87%8FOP%E4%B8%8E%E5%90%91%E9%87%8FOQ%E7%9A%84%E7%A7%AF%E7%9A%84%E5%80%BC%E5%BF%AB.%E5%90%91%E9%87%8F)
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与向量OQ的积的值快.向量
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与向量OQ的积的值
快.
向量
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与向量OQ的积的值快.向量
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