Let $\mathrm { E } : \frac { x ^ { 2 } } { \mathrm { a } ^ { 2 } } + \frac { y ^ { 2 } } { \mathrm {~b} ^ { 2 } } = 1 , \mathrm { a } > \mathrm { b }$ and $\mathrm { H } : \frac { x ^ { 2 } } { \mathrm {~A} ^ { 2 } } - \frac { y ^ { 2 } } { \mathrm {~B} ^ { 2 } } = 1$. Let the distance between the foci of E and the foci of $H$ be $2 \sqrt { 3 }$. If $a - A = 2$, and the ratio of the eccentricities of $E$ and $H$ is $\frac { 1 } { 3 }$, then the sum of the lengths of their latus rectums is equal to: (1) 10 (2) 9 (3) 8 (4) 7
Let $\mathrm { E } : \frac { x ^ { 2 } } { \mathrm { a } ^ { 2 } } + \frac { y ^ { 2 } } { \mathrm {~b} ^ { 2 } } = 1 , \mathrm { a } > \mathrm { b }$ and $\mathrm { H } : \frac { x ^ { 2 } } { \mathrm {~A} ^ { 2 } } - \frac { y ^ { 2 } } { \mathrm {~B} ^ { 2 } } = 1$. Let the distance between the foci of E and the foci of $H$ be $2 \sqrt { 3 }$. If $a - A = 2$, and the ratio of the eccentricities of $E$ and $H$ is $\frac { 1 } { 3 }$, then the sum of the lengths of their latus rectums is equal to:\\
(1) 10\\
(2) 9\\
(3) 8\\
(4) 7