Let the hyperbola H: x^2/a^2-y^2=1 and the ellipse E: 3 x^2+4 y^2=12 be such that the length of latus rectum of H is equal to the length of latus…

Let the hyperbola $\displaystyle H: \frac{x^2}{a^2}-y^2=1$ and the ellipse $\displaystyle E: 3 x^2+4 y^2=12$ be such that the length of latus rectum of $\displaystyle H$ is equal to the length of latus rectum of $\displaystyle E$. If $\displaystyle e_H$ and $\displaystyle e_E$ are the eccentricities of $\displaystyle H$ and $\displaystyle E$ respectively, then the value of $\displaystyle 12\left(e_H^2+e_E^2\right)$ is equal to \_\_\_\_.