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.

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.

The product of perpendiculars drawn from any point on a hyperbola to its asymptotes is

Two lines are intersecting if they have a common point; that common point is known as Point of Intersection.

4 lines and 5 circle are lie in a plane. Then all maximum no of points of intersection in this plane is -

If PN is the perpendicular from a point on a rectangular hyperbola xy=c^(2) to its asymptotes,then find the locus of the midpoint of PN

Two chords 2a and 2b of a circle are perpendicular to each other at a point they meet. If the distance between the centre of circle to this point is c ( clt radius of circle) then what is radius of circle.

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

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 a point of intersection of the circle & the parabola is: