If P and P denote the length of the perpendicular from a focus and the centre of an ellipse with semi - major axis of length a, respectively , on a tangent to the ellipse and r denotes the focal distance of the point , then

Prove that the product of the perpendicular from the foci on any tangent to an ellipse is equal to the square of the semi-minor axis.

If P_(1) and P_(2) are the lengths of the perpendiculars from any points on an ellipse to the major and minor axis and if a and b are lengths of semi-major and semi-minor axis respectively,then

If the normal at any point P on the ellipse cuts the major and minor axes in G and g respectively and C be the centre of the ellipse, then

P_(1) and P_(2) are the lengths of the perpendicular from the foci on the tangent of the ellipse and P_(3) and P_(4) are perpendiculars from extermities of major axis and P from the centre of the ellipse on the same tangent, then (P_(1)P_(2)-P^(2))/(P_(3)P_(4)-P^(2)) equals (where e is the eccentricity of the ellipse)

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 length of the latus rectum of an ellipse is 1/3 of the major axis. Its eccentricity is

If p is the length of the perpendicular from the focus S of the ellipse x^(2)/a^(2)+y^(2)/b^(2) = 1 to a tangent at a point P on the ellipse, then (2a)/(SP)-1=

Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lie on it

Consider an ellipse x^2/25+y^2/9=1 with centre c and a point P on it with eccentric angle pi/4. Nomal drawn at P intersects the major and minor axes in A and B respectively. N_1 and N_2 are the feet of the perpendiculars from the foci S_1 and S_2 respectively on the tangent at P and N is the foot of the perpendicular from the centre of the ellipse on the normal at P. Tangent at P intersects the axis of x at T.