Let E : \(\rm \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}\) = 1, a > b and H : \(\rm \frac{x^{2}}{A^{2}}-\frac{y^{2}}{B^{2}}\) = 1. Let the distance between the foci of E and the foci of H be 2√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
7
3
8
4
9