Coordinate Geometry: JEE Main 2021 Mathematics question

The point $P\left( { - 2\sqrt 6 ,\sqrt 3 } \right)$ lies on the hyperbola ${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$ having eccentricity ${{\sqrt 5 } \over 2}$. If the tangent and normal at P to the hyperbola intersect its conjugate axis at the point Q and R respectively, then QR is equal to :