A quadrilateral is inscribed in a parabola `y^2=4a x` and three of its sides pass through fixed points on the axis. Show that the fourth side also passes through a fixed point on the axis of the parabola.

From a variable point on the tangent at the vertex of a parabola y^(2)=4ax, a perpendicular is drawn to its chord of contact. Show that these variable perpendicular lines pass through a fixed point on the axis of the parabola.

The circle passing through the point (-1,0) and touching the y -axis at (0,2) also passes through the point:

Show that all chords of a parabola which subtend a right angle at the vertex pass through a fixed point on the axis of the curve.

Two chords are drawn through a fixed point 't' of the parabola y^(2)=4ax and are at right angles. Prove that the join of their other extremities passes through a fixed point.

LOL' and MOM' are two chords of parabola y^(2)=4ax with vertex A passing through a point O on its axis.Prove that the radical axis of the circles described on LL' and MM' as diameters passes though the vertex of the parabola.