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