## 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.)

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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

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Michael de Villiers, 14 March 2012.