JEE Main 2022 · 29 Jun · Shift 1, Mathematics question 28

Let $H:\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$, $a>0$, $b>0$, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is $4\left(2\sqrt2+\sqrt{14}\right)$. If the eccentricity H is $\dfrac{\sqrt{11}}2$, then the value of $a^2+b^2$ is equal to ______.