Circles are described on any focal chords of a parabola as diameters touches its directrix

Prove that the circle described on the focal chord of parabola as a diameter touches the directrix

The locus of the centre of the circle described on any focal chord of the parabola y^(2)=4ax as the diameter is

Circle described on the focal chord as diameter touches

A circle drawn on any focal chord of the parabola y^(2)=4ax as diameter cuts the parabola at two points 't' and 't' (other than the extremity of focal chord), then find the value of tt'.

Show that the tangents at the extremities of any focal chord of a parabola intersect at right angles at the directrix.

A circle of radius 4 drawn on a chord of the parabola y^(2)=8x as diameter touches the axis of the parabola. Then the slope of the chord is

Statmenet 1 : The point of intesection of the common chords of three circles described on the three sides of a triangle as diameter is orthocentre of the triangle. Statement-2 : The common chords of three circles taken two at a time are altitudes of the traingles.

The circles on the focal radii of a parabola as diameter touch: A) the tangent at the vertex B) the axis C) the directrix D) latus rectum

A circle, with its centre at the focus of the parabola y^2 =4ax and touching its directrix, intersects the parabola at the point (A) (a, 2a) (B) (a,-2a) (C) (a/2, a) (D) (a/2, 2a)

Prove that the length of a focal chord of a parabola varies inversely as the square of its distance from the vertex.