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.