Answer
III
Work Step by Step
$\frac{x^{2}}{4}-y^{2}=1$ is in the form $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ which is the standard equation of a hyperbola with x-axis as transverse axis. This implies that graph II and graph IV doesn't match with the given equation.
Comparing $\frac{x^{2}}{4}-y^{2}=1$ with $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$, we get a=2
a is the distance between the vertex and the center. In graph III, the distance between the center and the vertex is 2. Therefore, graph III is the correct match.
