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.

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

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.

If the normal at a point P to the hyperbola meets the transverse axis at G, and the value of SG/SP is 6, then the eccentricity of the hyperbola is (where S is focus of the hyperbola)

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

Certain telescopes contain both parabolic mirror and a hyperbolic mirror. In the telescope shown in figure the parabola and hyperbola share focus F_(1) which is 14m above the vertex of the parabola. The hyperbola's second focus F_(2) is 2m above the parabola's vertex. The vertex of the hyperbolic mirror is 1m below F_(1) . Position a coordinate systemm with the origin at the centre of the hyperbola and with the foci on the y-axis. then find the equation of the hyperbola.

Cross section of a Nuclear cooling towar is in the shape of a hyperbola with equation x^(2)/30^(2) - y^(2)/44^(2) = 1 . The towar is 150 m tall and the distance from the top of the towar to the centre of the hyperbola is half the distance from the base of the towar to the centre of the hyperbola. Find the diameter of the top and base of the tower.