Locus of foot of perpendicular from focus upon any tangent is tangent at vertex OR Image of focus in any tangent lies in Directrix

The locus of feet of perpendiculars from the focii upon any tangent is an auxilliary circle.

Prove that perpendicular drawn from locus upon any tangent of a parabola lies on the tangent at the vertex

The feet of the perpendicular drawn from focus upon any tangent to the parabola,y=x^(2)-2x-3 lies on

Find the locus of the foot of the perpendicular drawn from a fixed point to any tangent to a parabola.

Show that the locus of the foot of the perpendicular on a vaying tangent to an ellipse from either of its foci is a concentric circle