Each ellipse and hyperbola has a circle associated with it called the director circle. In this article, the author derives the equations of the circle for the ellipse and hyperbola through a different approach. Then the author concentrates on the director circle of the central conic given by the general quadratic equation. The content of this article could be used as enrichment to an analytic geometry course. The author discusses the director circle as a locus as well as the director circle of an arbitrary central conic. (Contains 5 figures.)