Conic sections and tangent circles

A straight line [b]m[/b] and a circle with centre [b]C[/b] are given. Let [b]A[/b] and [b]B[/b] be arbitrary points on the line [b]m[/b] and on the circle, respectively. [br][br][list][*]Ellipses and hyperbolas are generated by the family of perpendicular bisectors to [b]AB.[/b][br][/*][*]The parabolas are the envelope of the family of ellipses and hyperbolas defined by point [b]A.[/b][br][/*][*]The circles are tangent to the given circle and to the given line at [b]A[/b]. [br][/*][/list][br]Things to try:[br][br][list][*]Drag the points A, B or C. [br][/*][*]Activate boxes to show the other curves.[br][/*][/list]

Information: Conic sections and tangent circles