The angle between the asymptotes of the hyperbola x^2/16 - y^2/9 = 1

Question

The angle between the asymptotes of the hyperbola \(\frac{x^2}{16} - \frac{y^2}{9} =1\)

a. \(tan^{-1}\left(\frac 34\right)\)

b. \(tan^{-1}\left(\frac {24}7\right)\)

c. \(tan^{-1}\left(\frac 43\right)\)

d. \(tan^{-1}\left(\frac 45\right)\) 

Answer 1

Correct option is b. \(tan^{-1}\left(\frac {24}7\right)\) 

Equations of asymptotes are \(\frac{x}{4} - \frac{y}{3} =0\) and \(\frac{x}{4}+ \frac{y}{3} =0\)

lope of first asymptote is tanθ = \(\frac 34\)

\(\theta = tan^{-1} (\frac 34)\)

Angle between the asymptotes is \(2\theta = 2tan^{-1} (\frac 34)\)