WBJEE · Maths · Hyperbola
A hyperbola, having the transverse axis of length \(2 \sin \theta\) is confocal with the ellipse \(3 x^{2}+4 y^{2}=12\). It equation is
- A \(x^{2} \sin ^{2} \theta-y^{2} \cos ^{2} \theta=1\)
- B \(x^{2} \operatorname{cosec}^{2} \theta-y^{2} \sec ^{2} \theta=1\)
- C \(\left(x^{2}+y^{2}\right) \sin ^{2} \theta=1+y^{2}\)
- D \(x^{2} \operatorname{cosec}^{2} \theta=x^{2}+y^{2}+\sin ^{2} \theta\)
Answer & Solution
Correct Answer
(B) \(x^{2} \operatorname{cosec}^{2} \theta-y^{2} \sec ^{2} \theta=1\)
Step-by-step Solution
Detailed explanation
Given. \(2 a_{1}=2 \sin \theta\) \(\Rightarrow \quad a_{1}=\sin \theta\) and \(3 x^{2}+4 y^{2}=12\) \(\Rightarrow \quad \frac{x^{2}}{4}+\frac{y^{2}}{3}=1\) Here, \(a^{2}=4\) and \(b^{2}=3\) \(\therefore\) \(b^{2}=a^{2}\left(1-e^{2}\right)\) \(\Rightarrow\)…
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