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 :