AP EAMCET · Maths · Hyperbola
7. If \(\theta\) is the angle between the asymptotes of the hyperbola \(\frac{x^2}{a^2}-\frac{(y-2)^2}{4}=1\) and \(\cos \theta=\frac{5}{13}\), then \(a^2=\)
- A \(\frac{16}{3}\) or 18
- B \(\frac{16}{9}\) or 9
- C \(\frac{16}{7}\) or 6
- D \(\frac{16}{5}\) or 11
Answer & Solution
Correct Answer
(B) \(\frac{16}{9}\) or 9
Step-by-step Solution
Detailed explanation
Eqn. of hyperbola is \(\frac{x^2}{a^2}-\frac{(y-2)^2}{4}=1\) and \(\cos \theta=\frac{5}{13}\) \(\Rightarrow \quad \tan \theta=\frac{12}{5}\) ...(i) Angle between the asymptotes of hyperbola is \(\theta=\tan ^{-1}\left(\frac{2 \times 2 a}{a^2-4}\right)\)…
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