Let each of the two ellipses \({\text{E}}_{1}:\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1,\left(a>b\right)\) and \…

Let each of the two ellipses \({\text{E}}_{1}:\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1,\left(a>b\right)\) and \({\text{E}}_{2}:\frac{{x}^{2}}{{\text{ A}}^{2}}+\frac{{y}^{2}}{{\text{ B}}^{2}}=1,\left(\text{A}<\text{B}\right)\) have eccentricity \(\frac{4}{5}.\) Let the lengths of the latus rectum of \(E_1\) and \(E_2\) be \(l_1\) and \(l_2\) , respectively, such that \(2{l}_{1}^{2}=9{l}_{2}\). If the distance between the foci of \(E_1\) is 8, then the distance between the foci of \(E_2\) is

[JEE Main 2026, 24 Jan (Shift 1)]