Let the ellipse E: x^2/144+y^2/169=1 and the hyperbola H: x^2/16-y^2/(λ^2)=-1 have the same foci. If e and L respectively denote the eccentricity and…

Let the ellipse $\displaystyle \mathrm{E}: \frac{x^2}{144}+\frac{y^2}{169}=1$ and the hyperbola $\displaystyle \mathrm{H}: \frac{x^2}{16}-\frac{y^2}{\lambda^2}=-1$ have the same foci. If e and L respectively denote the eccentricity and the length of the latus rectum of H, then the value of $\displaystyle 24(\mathrm{e}+\mathrm{L})$ is :