Prove that image of the focus lies on directrix with respect to any tangent of parabola `y^2 = 4ax`

The focus of the parabola y^2= 4ax is :

Show that the locus of point of intersection of perpendicular tangents to the parabola y^2=4ax is the directrix x+a=0.

The locus of foot of perpendicular from the focus upon any tangent to the parabola y^(2) = 4ax is

The directrix of the parabola y^2=4ax is :

Show that the locus of point of intersection of perpendicular tangents to the parabola y(2)=4ax is the directrix x+a=0.

The focus of the parabola y^(2) = - 4ax is :

The locus of the mid-point of the line segment joining the focus to a moving point oh the parabola y^2 = 4ax is a parabola with directrix :