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

Prove that in an ellipse,the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet on the corresponding directrix.

The lengths of the perpendiculars from the focus and the extremities of a focal chord of a parabola on the tangent at the vertex form:

From vertex O ofthe parabola y^(2)=4ax perpendicular is drawn at a tangent to the parabola.If it meets the tangent and the parabola at point P and Q respectively then OP.OQ is equal to (A) constant (B) 1(C) -1(D) 2

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.

Product of perpendiculars drawn from the foci upon any tangent to the ellipse 3x^(2)+4y^(2)=12 is