Show that the eccentricity of any rectagular hyperbola is `sqrt(2)`.

Eccentricity of a rectangular hyperbola is -

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

Show that the eccentricities of the two hyperbolas (x^(2))/(16) - (y^(2))/(9) = 1 and (x^(2))/(64) - (y^(2))/(36) = 1 are equal.

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

let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal to that of the ellipse x^2+4y^2=4. if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is x^2/3-y^2/2=1 (b) a focus of the hyperbola is (2,0) (c) the eccentricity of the hyperbola is sqrt(5/3) (d) the equation of the hyperbola is x^2-3y^2=3

Show that the eccentricities of the two hyperbolas x^2/16-y^2/9=1 and x^2/64-y^2/36=1 are equal.

If the angle between the asymptotes of hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is (pi)/(3) , then the eccentricity of conjugate hyperbola is _________.

Show that the eccentricities of the hyperbolas x^2/16-y^2/9=1 and x^2/64-y^2/36=1 are equal.

Let L L ' be the latus rectum through the focus of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and A ' be the farther vertex. If A ' L L ' is equilateral, then the eccentricity of the hyperbola is (axes are coordinate axes).

The eccentricity of the hyperbola 4x^(2)-9y^(2) =36 is: