The director circle of x^{2+y}^2=$a^2$ is x^{2+y}^2=2$a^2$. It is the locus of the point from which the two tangents to the given circle are perpendicular. The director circle has the same centre but radius = asqrt(2). For a general circle with centre C and radius r, the director circle has centre C and radius rsqrt(2).