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.

The locus of the point of intersection of tangents drawn at the extremities of a focal chord to the parabola y^2=4ax is the curve

The locus of the point of intersection of tangents drawn at the extremities of normal chords to hyperbola xy = c^(2)

The locus of the point of intersection of tangents drawn at the extremities of a normal chord to the parabola y^2=4ax is the curve

The locus of the point of intersection of perpendicular tangents to the ellipse is called

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 .