Chord of contact of parabola

Tangents are drawn from any point on the directrix of y^(2)=16x to the parabola. If thelocus of the midpoint of chords of contact is a parabola, then its length (in units) of the latus rectum is

From a point on the axis of x common tangents are drawn to the parabola y^(2)=4x and the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1(agtbgt0) . If these tangents from an equilateral trianlge with their chord of contact w.r.t parabola, then set of exhaustive values of a is

If the distance of the point (alpha,2) from its chord of contact w.t.the parabola y^(2)=4x is 4, then find the value of alpha.

Find the locus of the middle points of the chords of contact of orthogonal tangents of the parabola y^(2)=4ax .

Chord of contact from a point

The chords of contact of all points on a line w.r.t the parabola y^(2)=4x are concurrent at the point (1,0) .The equation of the line

Find the equation of the chord of contact of the point (3,1) to the ellipse x^2+9y^2=9 . Also find the mid-point of this chord of contact.