What is the formula/method used to show that $ b=4$ in this hyperbola?

Question

Hyperbola

$\frac{x^2}{4}-\frac{y^2}{b^2}=1$

Asymptotes

$y=2x$ and $y=-2x$

Also given a point $A (2, 0)$ on the hyperbola (not sure if you need this though)

I have absolutely no idea how you would show that $b=4$ considering the limited information and there being $3$ unknowns, I am assuming that there is a formula?

Answer 1

Hint: Asymptote lines are: $\dfrac{x}{2} = \pm \dfrac{y}{b}$, and you had it as $y = \pm 2x$. Compare the slopes !