Circle described on the focal length as diameter touches the tangent at the vertex

Circle described on the focal chord as diameter touches the directrix.

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

Circle described on focal length as diameter always touches the auxilliary circle.

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

The locus of the mid-point of the line segment joining a point on the parabola Y^(2)=4ax and the point of contact of circle drawn on focal distance of the point as diameter with the tangent at the vertex, is

Prove that in a parabola,a circle of any focal radii of a point P(at^(2),2at) as diameter touches the tangent at the vertex and intercepts a chord of length a[(1+t^(2))]^(0.5) on a normal at the point P.

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.

prove that the circle drawn on any focal distance as diameter touches the auxiliary circle in an ellipse

A rectangle has two semi-circle described on its longer side as diameter,and the opposite side as tangent.Find the area enclosed between the semi-circles.

The lengths of the perpendiculars from the focus and the extremities of a focal chord of a parabola on the tangent at the vertex form: