Mathematics - Hyperbola Question with Solution | TestHub

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