Let $H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$, a > 0, b > 0, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is $4(2\sqrt 2 + \sqrt {14} )$. If the eccentricity H is ${{\sqrt {11} } \over 2}$, then the value of a2 + b2 is equal to __________.

Question

Let $H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$, a > 0, b > 0, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is $4(2\sqrt 2 + \sqrt {14} )$. If the eccentricity H is ${{\sqrt {11} } \over 2}$, then the value of a² + b² is equal to __________.

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