T is the pole of the chord PQ , prove that the perpendiculars from P, T, and Q upon any tangent to the parabola are in geometrical progression.

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

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

P is a point on the parabola y^(2)=4ax whose ordinate is equal to its abscissa and PQ is focal chord, R and S are the feet of the perpendiculars from P and Q respectively on the tangent at the vertex, T is the foot of the perpendicular from Q to PR, area of the triangle PTQ is

If length of focal chord PQ is l, and p is the perpendicular distance of PQ from the vertex of the parabola,then prove that l prop(1)/(p^(2))

Through the vertex O of the parabola y^(2) = 4ax , a perpendicular is drawn to any tangent meeting it at P and the parabola at Q. Then OP, 2a and OQ are in