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

Assertion (A) : Orthocentre of the triangle formed by any three tangents to the parabola lies on the directrix of the parabola Reason ® : The orthocentre of the triangle formed by the tangents at t_1, t_2 ,t_3 to the parabola y^(2) =4ax is (-a ( t_1+t_2+t_3+t_1t_2t_3) )

Show that the area of the triangle formed by the tangent at any point on the curve xy=c, (c ne 0), with the coordinate axes is constant.