Ellipse

Let the eccentricity of the ellipse \({x^2} + {a^2}{y^2} = 25{a^2}\) be b times the eccentricity of the hyperbola \({x^2} - {a^2}{y^2} = 5\), where a is the minimum distance between the curves y = e^x and y = log_ex. Then \({a^2} + {1 \over {{b^2}}}\) is equal to :