Nomenclature of parabola and Chord of parabola

Introduction to parabola and Nomenclature of parabola

Let y^(2)=4ax be a parabola and PQ be a focal chord of parabola.Let T be the point of intersection of tangents at P and Q. Then

A circle of radius r drawn on a chord of the parabola y^(2)=4ax as diameter touches theaxis of the parabola.Prove that the slope of the chord is (2a)/(r)

The maximum possible area bounded by the parabola y=x^2+x+10 and a chord of the parabola of length 1 is

The endpoints of two normal chords of a parabola are concyclic.Then the tangents at the feet of the normals will intersect (a) at tangent at vertex of the parabola (b) axis of the parabola (c) directrix of the parabola (d) none of these

Find the locus of midpoint normal chord of the parabola y^(2)=4ax

Find the locus of the midpoint of normal chord of parabola y^(2)=4ax