The point \( P(-2 \sqrt{6}, \sqrt{3}) \) lies on the hyperbola \( \...

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The point \( P(-2 \sqrt{6}, \sqrt{3}) \) lies on the hyperbola
\( \mathrm{P} \)
W \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) having eccentricity \( \frac{\sqrt{5}}{2} \). If the tangent and normal at \( P \) to the hyperbola intersect its conjugate axis at the point \( Q \) and \( R \) respectively, then \( Q R \) is equal to
(1) \( 4 \sqrt{3} \)
(2) 6
(3) \( 6 \sqrt{3} \)
(4) \( 3 \sqrt{6} \)
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