Question

I: The angle between the asymptotes of the hyperbola $x^2-3y^2=3$ is ${30}^0$
II:The angle between the asymptotes of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is $2ta{n}^{-1}\frac{b}{a}$.
Which of the above statement is correct?

• A. Only I
• B. Only II
• C. Both I and II
• D. Neither I nor II

Answer 1

The correct option is B Only II

The asymptotes of hyperbola are $\frac{x}{a}\pm \frac{y}{b}=0$

Then angle between straight lines is ${\tan }^{-1}\left|\frac{\frac{b}{a}-\left(\frac{-b}{a}\right)}{1-\frac{b^2}{a^2}}\right|=2{\tan }^{-1}\frac{b}{a}$