X^2+y^2-x+y=0 化成圆的标准方程

2026-05-19 15:41:10
推荐回答(4个)
回答1:

设 圆的标准方程为(X-a)^2+(y-b)^2=1....(1)
上式展开后得:X^2-2ax+a^2+y^2+2by+b^2=1
与原方程比较后可得:-2a=-1 -2b=1
即 a=1/2 b=-1/2 a^=1/4,b^2=1/4 代入(1)后得
(X-1/2)^2+(y+1/2)^2=1./2.

回答2:

(X-1/2)的平方+(y+1/2)的平方=1/2

回答3:

圆心(-1/2,1/2) r=√2/2

(x-1/2)^2+(y+1/2)^2=1/2

回答4:

(X-1/2)^2+(Y+1/2)^2=1/2