If the eccentricity is zero, show that the ellipse becomes a circle.

Let the major axis of a standard ellipse equals the transverse axis of a standard hyperbola and their director circles have radius equal to 2R and R respectively. If e_(1) and e_(2) , are the eccentricities of the ellipse and hyperbola then the correct relation is

Let a hyperbola passes through the focus of the ellipse (x^(2))/(25)+(y^(2))/(16)=1 . The transverse and conjugate axes of this hyperbola coincide with the major and minor axis of the given ellipse. Also, the product of the eccentricities of the given ellipse and hyperbola is 1. Then,

Find the eccentricity of the ellipse if : the latus-rectum is one half of its minor axis.

Find the eccentricity of the ellipse if : the latus-rectum is one half of its major axis.

Find the eccentricity of the ellipse if : the distance between the foci is equal to the length of latus-rectum.

If the eccentricity of an ellipse is 1/sqrt2 , then its latusrectum is equal to its

An ellipse intersects the hyperbola 2x^2- 2y^2 = 1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the co-ordinate axes, then :

A series of concentric ellipses E_1,E_2, E_3..., E_n are drawn such that E touches the extremities of the major axis of E_(n-1) , and the foci of E_n coincide with the extremities of minor axis of E_(n-1) If the eccentricity of the ellipses is independent of n, then the value of the eccentricity, is