Let the sum of the focal distances of the point P (4,3) on the hyperbola H: x^2/(a^2)-y^2/(b^2)=1 be 8 √(5/3). If for H, the length of the latus…

Let the sum of the focal distances of the point $\displaystyle \mathrm{P}(4,3)$ on the hyperbola $\displaystyle \mathrm{H}: \frac{x^2}{\mathrm{a}^2}-\frac{y^2}{\mathrm{~b}^2}=1$ be $\displaystyle 8 \sqrt{\frac{5}{3}}$. If for H, the length of the latus rectum is $\displaystyle l$ and the product of the focal distances of the point P is m , then $\displaystyle 9 l^2+6 \mathrm{~m}$ is equal to :