What is the eccentricity of a rectangular hyperbola.

Statement-I If eccentricity of a hyperbola is 2, then eccentricity of its conjugate hyperbola is (2)/(sqrt(3)) . Statement-II if e and e_1 are the eccentricities of two conjugate hyperbolas, then ee_1gt1 .

The equation of the line passing through the centre of a rectangular hyperbola is x-y-1=0 . If one of its asymptotoes is 3x-4y-6=0 , the equation of the other asymptote is

Statement-I A hyperbola whose asymptotes include (pi)/(3) is said to be equilateral hyperbola. Statement-II The eccentricity of an equilateral hyperbola is sqrt(2).

A triangle has its vertices on a rectangular hyperbola. Prove that the orthocentre of the triangle also lies on the same hyperbola.

The tangent at the point P of a rectangular hyperbola meets the asymptotes at L and M and C is the centre of the hyperbola. Prove that PL=PM=PC .

Statement-I (5)/(3) and (5)/(4) are the eccentricities of two conjugate hyperbolas. Statement-II If e_1 and e_2 are the eccentricities of two conjugate hyperbolas, then e_1e_2gt1 .

Let P(6, 3) be a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1. If the normal at point P intersects the x-axis at (9, 0), then find the eccentricity of the hyperbola.

ABC is a triangle such that angleABC=2angleBAC . If AB is fixed and locus of C is a hyperbola, then the eccentricity of the hyperbola is

sqrt 2009/3 (x^2-y^2)=1 , then eccentricity of the hyperbola is :