The perpendicular from the foci on either asymptote meets it at the same point as the corresponding directrix and the common points of intersection lie on the auxiliary circle

The perpendicular from the focii on either assymptotes meet it at the same point as the same directrix and the common point of intersection lie on auxilliary circle.

The point of intersection of the asymptotes with the directrices lie on

The point of intersection of the asymptotes with the directrices lie on

Show that the tangent at any point on an ellipse and the tangent at the corresponding point on its auxiliary circle intersect on the major axis.

Show that the locus of the feet of the perpendiculars drawn from the foci to any tangent of the ellipse is the auxiliary circle

Prove that in an ellipse, the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet on the corresponding directrix.

Prove that in an ellipse the perpendicular from focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet on the corresponding directrix.

Prove that in an ellipse,the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet on the corresponding directrix.

Prove that in an ellipse, the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet on the corresponding directrix.

Prove that in an ellipse, the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet on the corresponding directrix.