AP EAMCET · Maths · Hyperbola
If \(\theta\) is the acute angle between the asymptotes of a hyperbola \(7 \mathrm{x}^2-9 \mathrm{y}^2=63\), then \(\cos \theta=\)
- A \(\frac{1}{4}\)
- B \(\frac{3}{4}\)
- C \(\frac{1}{8}\)
- D \(\frac{4}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{8}\)
Step-by-step Solution
Detailed explanation
\(\frac{7x^2}{63} - \frac{9y^2}{63} = 1 \implies \frac{x^2}{9} - \frac{y^2}{7} = 1\) \(a^2=9, b^2=7 \implies a=3, b=\sqrt{7}\) \(m_1 = \frac{b}{a} = \frac{\sqrt{7}}{3}, m_2 = -\frac{b}{a} = -\frac{\sqrt{7}}{3}\)…
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