If the eccentricity of the hyperbola x^2 a^2 - y^2 b^2 =1 is , then area of the triangle formed by the asymptotes of the hyperbola with any of its tangent is

Step-by-step solution

x^2 a^2 - y^2 b^2 =1 We know, area of triangle formed by the asymptotes of the hyperbola with any of its tangent is a b . Now, e^2= ^2 aligned & 1+ b^2 a^2 =1+ ^2 b^2 a^2 = ^2 & b^2 ^2 =a^2 b^4 ^2 =a^2 b^2 & b^2 | | =a b aligned