The equation x^2+y2-4x+2y=b describe a circle
\(x^2+y^2-4x+2y=b\implies~x^2-4x+4+y^2+2y+1=b+5\implies~(x-2)^2+(y+1)^2=b+5\)This describes a circle centered at \((2,-1)\) with radius \(\sqrt{b+5}\).
