Find the locus of the points of trisection of double ordinate of a parabola `y^(2)=4ax (agt0)`

Find the locus of the points of trisection of double ordinate of a parabola y^(2)=4x (agt0)

The locus of the point of intersection of perpendicular tangents to the parabola y^(2)=4ax is

The locus of the midpoints of the focal chords 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 the point of intersection of two tangents to the parabola y^(2)=4ax which make complementary angles with the axis of the parabola is