JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
For \(0<\theta<\pi / 2\), if the eccentricity of the hyperbola \(\mathrm{x}^2-\mathrm{y}^2 \operatorname{cosec}^2 \theta=5\) is \(\sqrt{7}\) times eccentricity of the ellipse \(x^2 \operatorname{cosec}^2 \theta+y^2=5\), then the value of \(\theta\) is :
- A \(\frac{\pi}{6}\)
- B \(\frac{5 \pi}{12}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
\(e_h=\sqrt{1+\sin ^2 \theta}\) \(e_c=\sqrt{1-\sin ^2 \theta}\) \(e_h=\sqrt{7} e_c\) \(1+\sin ^2 \theta=7\left(1-\sin ^2 \theta\right)\) \(1+\sin ^2 \theta=7\left(1-\sin ^2 \theta\right)\) \(\sin ^2 \theta=\frac{6}{8}=\frac{3}{4}\) \(\sin \theta=\frac{\sqrt{3}}{2}\)…
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