Show that the tangents at the extremities of any focal chord of a parabola intersect at right angles at the directrix.

prove that the locus of the point of intersection of the tangents at the extremities of any chord of the parabola y^2 = 4ax which subtends a right angle at the vertes is x+4a=0 .

Prove that the tangent at one extremity of the focal chord of a parabola is parallel to the normal at the other extremity.

Prove that the tangents at the extremities of any chord make equal angles with the chord.

If the tangents at the extremities of a focal chord of the parabola x^(2)=4ay meet the tangent at the vertex at points whose abcissac are x_(1) and x_(2) then x_(1)x_(2)=

If the tangent at the extrenities of a chord PQ of a parabola intersect at T, then the distances of the focus of the parabola from the points P.T. Q are in

Show that the locus of the point of intersection of the tangents at the extremities of any focal chord of an ellipse is the directrix corresponding to the focus.

Show that the tangents at the extremities of the latus rectum of an ellipse intersect on the corresponding directrix.