题目内容
以两点A(-3,-1)和B(5,5)为直径端点的圆的方程是_________.
(x-1)2+(y-2)2=25
解析:设P(x,y)是所求圆上任意一点.∵ A、B是直径的端点,∴
·
=0.又
=(-3-x,-1-y),
=(5-x,5-y).由
·
=0(-3-x)·(5-x)+(-1-y)(5-y)=0x2-2x+y2-4y-20=0(x-1)2+(y-2)2=25.
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题目内容
以两点A(-3,-1)和B(5,5)为直径端点的圆的方程是_________.
(x-1)2+(y-2)2=25
解析:设P(x,y)是所求圆上任意一点.∵ A、B是直径的端点,∴
·
=0.又
=(-3-x,-1-y),
=(5-x,5-y).由
·
=0(-3-x)·(5-x)+(-1-y)(5-y)=0x2-2x+y2-4y-20=0(x-1)2+(y-2)2=25.