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

Prove that perpendicular drawn from focus 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

Show that the locus of the feet of the perpendiculars drawn from the foci to any tangent of the ellipse is the auxiliary circle

Prove that the locus of the foot of the perpendicular drawn from the focus of the parabola y ^(2) = 4 ax upon any tangent to its is the tangent at the vertex.

If S be the focus and SH be perpendicular to the tangent at P , then prove that H lies on the tangent at the vertex and SH^2 = OS.SP , where O is the vertex of the parabola.

If S be the focus and SH be perpendicular to the tangent at P , then prove that H lies on the tangent at the vertex and SH^2 = OS.SP , where O is the vertex of the parabola.