Question

Angle between asymptotes of the hyperbola $3x^2-y{z}^2=3$ is

• A. $\frac{\pi }{3}$
• B. $\frac{2\pi }{3}$
• C. $\frac{\pi }{6}$
• D. $\frac{3\pi }{4}$

Answer 1

The correct option is B $\frac{2\pi }{3}$

Equation of the pair of Asymptotes is $3x^2-y^2+k=0$ But passes through origin
$\Rightarrow k=0$
$\therefore$ Asymptotes are $3x^2-y^2=0$
$\therefore$ Angle α between them $\alpha =2Ta{n}^{-1}\left\{\frac{2\sqrt{0+3}}{3-1}\right\}\therefore \alpha =\frac{2\pi }{3}$