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

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

Circle described on the focal chord as diameter touches

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

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

Prove that the tangent at one extremity of the focal chord of a parabola is parallel to the normal at the other extremity.

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

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 radical centre of the circles drawn on the focal chords of y^(2)=4ax as diameters, is

Consider a circle with its centre lying on the focus of the parabola, y^2=2px such that it touches the directrix of the parabola. Then a point of intersection of the circle & the parabola is:

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