Let \( H: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1, a0, b0 \), be ...

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Let \( H: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1, a0, b0 \), be a hyperbola
P 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 \( \frac{\sqrt{11}}{2} \), then the value of \( a^{2}+b^{2} \) is equal to
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