Coordinate Geometry: JEE Main 2022 Mathematics question

Let the eccentricity of the hyperbola ${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$ be ${5 \over 4}$. If the equation of the normal at the point $\left( {{8 \over {\sqrt {5} }},{{12} \over {5}}} \right)$ on the hyperbola is $8\sqrt 5 x + \beta y = \lambda$, then $\lambda$ $-$ $\beta$ is equal to ___________.