What is the distance between the foci of the hyperbola x^{2}-4y^{2}=1?

Explanation

Rewrite the hyperbola in standard form: \frac{x^2}{1} - \frac{y^2}{1/4} = 1. Here, a^2 = 1 and b^2 = 1/4. For a hyperbola, the relation is c^2 = a^2 + b^2 = 1 + 1/4 = 5/4, so c = \frac{\sqrt{5}}{2}. The distance between the foci is 2c = \sqrt{5}.

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