Coordinate Geometry: JEE Main 2022 Mathematics question

Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola ${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$. Let e' and l' respectively be the eccentricity and length of the latus rectum of its conjugate hyperbola. If ${e^2} = {{11} \over {14}}l$ and ${\left( {e'} \right)^2} = {{11} \over 8}l'$, then the value of $77a + 44b$ is equal to :