The tangents at the ends of a focal chord of a parabola `y^(2)=4ax ` intersect on the directrix at an angle of

The locus of the midpoints of the focal chords of the parabola y^(2)=4ax is

The locus of middle points of normal chords of the parabola y^(2) = 4ax is

Show that the locus of point of intersection of normals at the ends of a focal chord of the parabola y^(2) = 4ax is y^(2)= a(x- 3a).