Hyperbola

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 :