The point \(P(-2\sqrt{6},\sqrt{3})\) lies on the hyperbola \(\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1\) having …

The point \(P(-2\sqrt{6},\sqrt{3})\) lies on the hyperbola \(\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1\) having eccentricity \(\frac{\sqrt{5}}{2}\). 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:

[JEE Main 2021, 26 Aug (Shift 2)]