Q65 / 180 · COMEDK 2012 · Mathematics

The angle between two asymptotes of the hyperbola $\frac{x^{2}}{25}-\frac{y^{2}}{16}=1$ is

  • A
    $\tan ^{-1} \frac{4}{5}$
  • Correct answer
    B
    $2 \tan ^{-1} \frac{4}{5}$
  • C
    $2 \tan ^{-1} \frac{5}{4}$
  • D
    $\pi-2 \tan ^{-1} \frac{4}{5}$

Solution

Given, equation of hyperbola is $\frac{x^{2}}{25}-\frac{y^{2}}{16}=1$ Here, $\quad a^{2}=25 \Rightarrow a=5$ $b^{2}=16 \Rightarrow b=4$ Now, $\theta=2 \tan ^{-1}\left(\frac{b}{a}\right)=2 \tan ^{-1}\left(\frac{4}{5}\right)$

Hence, the correct answer is option: 'B'.

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