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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?

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Thomas Winkworth
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    you divide the equation out by $x^2.$ you get $\frac{1}{4} - \frac{y^2}{b^2x^2} = \frac{1}{x^2}.$ now, let $x\to \infty$ to see the asymptote. – abel Feb 11 '15 at 01:40

1 Answers1

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

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