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

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.

Circle described on the focal chord as diameter touches

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

Prove that the circle on a focal radius of a parabola, as diameter touches the tangent at the vertex.

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

The tangent at a point P on an ellipse intersects the major axis at T ,a n dN is the foot of the perpendicular from P to the same axis. Show that the circle drawn on N T as diameter intersects the auxiliary circle orthogonally.