[color=#ff00ff][b]Definition of an Ellipse: [br][/b][/color][br]An [color=#ff00ff][b]ellipse is a locus (set of points that satisfy a certain condition) in the plane, for which the sum of the distances from 2 other fixed points, called foci, is constant.[/b][/color] In the applet, [i]A[/i] and [i]B[/i] are foci. [br][br]1) Since the radius of a circle is constant, we know that [i]AC[/i] = constant. [br]2) Thus, this implies [i]AD + CD [/i]= a constant value. [br]3) Since p is the perpendicular bisector of the segment with endpoints [i]B[/i] and [i]C[/i], we know [i]BD[/i] = [i]CD.[br] (Why?)[br][/i]4) Thus, given (2) and (3), we can say that [i]AD[/i] + [i]BD[/i] = a constant value.