Parabola locus theorem

What do you observe regarding the feet of the perpendiculars from the focus of a parabola to all possible tangents to the parabola?

Drag point A and observe the locus of point B. (Please note that there might be a delay before point A becomes active to drag.)

Please install Java (version 1.4 or later) to use JavaSketchpad applets.

Parabola locus theorem

Can you explain why (prove that) the feet of the perpendiculars from the focus of a parabola to all possible tangents to the parabola are collinear - specifically lying on a straight line tangent to the parabola at its vertex? If stuck, click on Hint

Michael de Villiers, 14 March 2012.