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

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

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

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

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

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

If C is a circle described on the focal chord of the parabola y^(2)=4x as diameter which is inclined at an angle of 45^(@) with the axis,then the

Prove that the diameter is the greatest chord in a circle.

Prove that the chords inclined on the same angle to the radius or diameter of a circle are equal in length.