Hyperbola with a Circle Locus

Given: point C is a point on circle O. point F is any point (inside or outside of circle O). line DL is the perpendicular bisector of FC. point L is on line OC. As point C moves around circle O, point L moves. What is its locus? Why is its locus what it is? Click the box to the left of "Show Trace" to trace point L. Click the box to the left of "Show Locus" to show the locus of point L Click the play/pause botton in the lower left to start/stop animating point C. Move point F around to see how the locus changes. What happens to the locus as point F moves?