$\begin{array}{ll}\frac{x^2}{a^2}-\frac{y^2}{1}=1 & \frac{x^2}{4}+\frac{y^2}{3}=1 \\ e_H=\sqrt{1+\frac{1}{a^2}} & e_E=\sqrt{1-\frac{3}{4}}=\frac{1}{2} \\ \ell . R .=\frac{2}{a} & \ell . R .=\frac{2 \times 3}{2}=3 \\ \frac{2}{a}=3 & \\ a=\frac{2}{3} & \\ e_H=\sqrt{1+\frac{9}{4}}=\frac{\sqrt{13}}{2} & \\ 12\left(e_H^2+e_E^2\right)=12\left(\frac{13}{4}+\frac{1}{4}\right) & \\ =\frac{12 \times 14}{4}=42 & \end{array}$