If the latus rectum and the transverse axis of a hyperbola are equal, show that it is a rectangular hyperbola.

Eccentricity of a rectangular hyperbola is -

If asymptotes of hyperbola bisect the angles between the transverse axis and conjugate axis of hyperbola, then what is eccentricity of hyperbola?

The length of the transverse axis of the hyperbola 9y^(2) - 4x^(2) = 36 is -

If the latus rectum of a hyperbola forms an equilateral triangle with the vertex at the center of the hyperbola ,then find the eccentricity of the hyperbola.

An ellipse and a hyperbola are confocal (have the same focus) and the conjugate axis of the hyperbola is equal to the minor axis of the ellipse. If e_1a n de_2 are the eccentricities of the ellipse and the hyperbola, respectively, then prove that 1/(e_1^2)+1/(e_2^2)=2 .

If the latus rectum of a hyperbola is equal to half of its transverse axis, then its eccentricity is -

If the length of conjugate axis and the length of latus rectum of a hyperbola are equal, find its eccentricity.

P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , and N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, then OT.ON is equal to

A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is