怎么把圆方程:x方+y方-x+2y=0 化简成标准式:(x-1/2)方+(y+1)方=5/4 辛苦.

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怎么把圆方程:x方+y方-x+2y=0 化简成标准式:(x-1/2)方+(y+1)方=5/4 辛苦.
怎么把圆方程:x方+y方-x+2y=0 化简成标准式:(x-1/2)方+(y+1)方=5/4 辛苦.

怎么把圆方程:x方+y方-x+2y=0 化简成标准式:(x-1/2)方+(y+1)方=5/4 辛苦.
x^2+y^2-x+2y=0
=>
x^2-x+1/4+y^2+2y+1=1/4+1
=>
(x-1/2)^2+(y+1)^2=5/4
这就是所谓的配方法

:x方+y方-x+2y=0
(x-2*1/2x+1/4)-1/4+(y+2y+1)-1=0
(x-1/2)^2+(y+1)^2=5/4

配方
x方+y方-x+2y=0
(x^2-x+1/4)+(y^2+2y+1)-1/4-1=0
(x-1/2)^2+(y-1)^2=5/4

主要利用配方法,配成一个完全平方式
x^2-x+(1/2)^2+y^2+2y+1^2-1/4-1=0
(x-1/2)^2+(y+1)^2=5/4

x方+y方-x+2y=(x方-x)+(y方+2y)=[x方-2*(1/2)x]+(y方+2*1y)=(x-1/2)方-1/4+(y-1)方-1=(x-1/2)方+(y+1)方=5/4

x^2+y^2-x+2y=0
(x^2-x+1/4)+(y^2+2y+1)-1/4-1=0
(x-1/2)^2+(y-1)^2=5/4