At some point P on the ellipse the segments ss' subtends a right angle then its eccentricity

If the lines joining the foci of an ellipse to an end of its minor axis are at right angles , then the eccentricity of the ellipse is e =

The tangent at a point P(a cos phi,b sin phi) of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets its auxiliary circle at two points,the chord joining which subtends a right angle at the center.Find the eccentricity of the ellipse.

If z_(0),z_(1) represent points P and Q on the circle |z-1|=1 taken in anticlockwise sense such that the line segment PQ subtends a right angle at the center of the circle, then z_(1)=

A circle of maximum area is inscribed in an ellipse. If p is the probability that a point within the ellipse chosen at random lies outside the circle, then the eccentricity of the ellipse is

Prove that the portion of the tangent to an ellipse intercepted between the ellipse and the directrix subtends a right angle at the corresponding focus.

A and B are two fixed points and the line segment AB always subtends an acute angle at a variable point P .Show that the locus of the point P is a circle.

The intercept made by the auxiliary circle of the ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b gt 1) on any tangent to the ellipse, subtends a right angle at its ceotre if

If the segment joining the points (a,b),(c,d) subtends a right angle at the origin,then

The tangent at the point alpha on a standard ellipse meets the auxiliary circle in two points which subtends a right angle at the centre. Show that the eccentricity of the ellipse is (1+ sin^2aplha)^-1/2 .