Parabola - Geometric Definition II

Given: point D is a point line AB. point L is the intersection of the perpendicular bisector of segment FD and the line through point D perpendicular to line AB. As point D moves along line AB, point L moves. What is its locus? Why is its locus what it is? Click the box to the left of "Show Trace of point L" to trace point L. Click the box to the left of "Show Locus of point L" to see the locus of point L. Click the play/pause botton in the lower left to start/stop animating point D. Move points F, A, and/or B around to see how the locus changes.