Question

The eccentricity of the hyperbola whose asymptotes are $3x+4y=10$ and $4x-3y=5$ is

• A. $\sqrt{3}$
• B. $\sqrt{2}$
• C. $\sqrt{5}$
• D. $\sqrt{6}$

Answer 1

The correct option is B $\sqrt{2}$

If $\theta$ is angle between asymptotes, then
$\theta ={\tan }^{-1}\frac{b}{a}$
$\Rightarrow \tan \frac{\theta }{2}=\frac{b}{a}$
$\Rightarrow \tan \frac{\pi }{4}=\frac{b}{a}$
($\because$ given lines are perpendicular )
$\therefore a=b$
$\Rightarrow e=\sqrt{2}$ which is a rectangular hyperbola.