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

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.

If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 such that O P Q is an equilateral triangle, O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.

The eccentricity of the hyperbola x^2-y^2=4 is

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

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

PQ is the double ordinate of the hyperbola x^2/a^2-y^2/b^2=1 and O is the centre of the hyperbola. If triangle OPQ is an equilateral triangle, then show that the eccentricity of this hyperbola is e) e^2 >4/3

If the latus rectum subtends a right angle at the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then find its eccentricity.

Find the length of the transverse and conjugate axes of the hyperbola 9x^(2) - 16y^(2) = 144 . Write down the equation of the hyperbola conjugate to it and find the eccentricities of both the hyperbolas.

If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is

The locus of the foot of perpendicular from my focus of a hyperbola upon any tangent to the hyperbola is the auxiliary circle of the hyperbola. Consider the foci of a hyperbola as (-3, -2) and (5,6) and the foot of perpendicular from the focus (5, 6) upon a tangent to the hyperbola as (2, 5). The conjugate axis of the hyperbola is