The standard equation (x-h)^2 + (y-k)^2 = $r^2$ has centre (h,k) and radius r. Expanding gives $x^2$ + $y^2$ - 2hx - 2ky + (h^{2+k}^{2-r}^2) = 0. Comparing with the general form $x^2$ + $y^2$ + 2gx + 2fy + c = 0: g = -h, f = -k, c = h^{2+k}^{2-r}^2. So centre = (-g,-f) and radius = sqrt(g^{2+f}^{2-c}). The general form must have equal coefficients of $x^2$ and $y^2$ (both 1) and no xy term to represent a circle.