Diameter form: if (x1,y1) and (x2,y2) are endpoints of a diameter, the circle is (x-x1)(x-x2) + (y-y1)(y-y2) = 0. This automatically gives the correct centre (midpoint) and radius (half the diameter). Parametric form: any point on x^{2+y}^2=$a^2$ is (acos(theta), asin(theta)). For (x-h)^2+(y-k)^2=$r^2$: point is (h+rcos(theta), k+rsin(theta)).