Let the latus ractum of the hyperbola x^2/9-y^2/b^2=1 subtend an angle of (π)/3 at the centre of the hyperbola. If b^2 is equal to l/m(1+√ n ), where…

Let the latus ractum of the hyperbola $\displaystyle \frac{x^2}{9}-\frac{y^2}{b^2}=1$ subtend an angle of $\displaystyle \frac{\pi}{3}$ at the centre of the hyperbola. If $\displaystyle b^2$ is equal to $\displaystyle \frac{l}{m}(1+\sqrt{n})$, where $\displaystyle l$ and $\displaystyle m$ are co-prime numbers, then $\displaystyle l^2+m^2+n^2$ is equal to $\displaystyle \_\_\_\_$.