How can I transform the circle $x^2+y^2+a x+b y+c=0$ into $ (x-A)^2+(y-B)^2+C=0$

I want Mathematica to put the circle given by $x^2+y^2+a x+b y+c=0$ into the standard form $(x-A)^2+(y-B)^2+C=0$, but I haven’t been able to.

I tried:

Solve(
  CoefficientList(x^2 + y^2 + a x + b y + c = 0, x) == 
  CoefficientList((x - A)^2 + (y - B)^2 + C = 0, 
  {x, y}))

but it’s wrong and I don’t understand why.