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

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

From a variable point on the tangent at the vertex of a parabola y^(2)=4ax, a perpendicular is drawn to its chord of contact. Show that these variable perpendicular lines pass through a fixed point on the axis of the parabola.

Through the vertex O of the parabola y^(2)=4ax, variable chords O Pand OQ are drawn at right angles.If the variables chord PQ intersects the axis of x at R, then distance OR

Through the vertex of the parabola y^(2)=4ax , chords OA and OB are drawn at right angles to each other . For all positions of the point A, the chord AB meets the axis of the parabola at a fixed point . Coordinates of the fixed point are :

The tangents to the parabola y^(2)=4ax at the vertex V and any point P meet at Q. If S is the focus,then prove that SP.SQ, and SV are in G.

Through the vertex O of a parabola y^(2) = 4x chords OP and OQ are drawn at right angles to one another. Show that for all position of P, PQ cuts the axis of the parabola at a fixed point.

A straight line is drawn parallel to the x-axis to bisect an ordinate PN of the parabola y^(2) = 4ax and to meet the curve at Q. Moreever , NQ meets the tangent at the vertex A of the parabola at T. AT= Knp , then k is equal to

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