The orthocenter of a triangle formed by 3 tangents to a parabola `y^2=4ax` lies on

Show that the orthocentre of a triangle formed by three tangents to a parabola lies on the directrix.

Prove that the orthocentre of the triangle formed by any three tangents to a parabola lies on the directrix of the parabola

Prove that the orthocentre of the triangle formed by any three tangents to a parabola lies on the directrix of the parabola

Prove that the area of triangle formed by the tangents to the parabola y^(2)=4ax from the point (x_(1),y_(1)) and the chord of contact is 1/(2a)(y_(1)^(2)-4ax_(1))^(3//2) sq. units.