JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The point \(\mathrm{P}(-2 \sqrt{6}, \sqrt{3})\) 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 \(\mathrm{P}\) to the hyperbola intersect its conjugate axis at the point \(\mathrm{Q}\) and \(\mathrm{R}\) respectively, then \(QR\) is equal to :
- A \(4 \sqrt{3}\)
- B \(6\)
- C \(6 \sqrt{3}\)
- D \(3 \sqrt{6}\)
Answer & Solution
Correct Answer
(D) \(3 \sqrt{6}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{P}(-2 \sqrt{6}, \sqrt{3})\) lies on hyperbola \(\mathrm{e}=\frac{\sqrt{5}}{2} \Rightarrow \mathrm{b}^{2}=\mathrm{a}^{2}\left(\frac{5}{4}-1\right) \Rightarrow 4 \mathrm{~b}^{2}=\mathrm{a}^{2}\)…
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