Question

The angle between asymptotes of $\frac{x^{2}}{16}-\frac{y^{2}}{9}=1$

• A. $\tan ^{-1}\left(\frac{7}{24}\right)$
• B. $\tan ^{-1}\left(\frac{24}{7}\right)$
• C. $\pi / 4$
• D. $\pi / 3$

Answer 1

Answer: (B)

$\theta=2 \tan ^{-1}\left(\frac{b}{a}\right)=2 \tan ^{-1}\left(\frac{3}{4}\right)$
$=\tan ^{-1}\left(\frac{2(3 / 4)}{1-9 / 16}\right)=\tan ^{-1}\left(\frac{3 / 2}{7 / 16}\right)$
$\therefore \theta=\tan ^{-1}\left(\frac{24}{7}\right)$