91Ó°ÊÓ

The graph of the hyperbola is,

We need to find the equation of the hyperbola.

The equation of the hyperbola having its centre at $(0,0)$, foci at $(Â\pm c,0)$and vertices at $(Â\pm a,0)$and whose transverse axis is the $x-$axis is, $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, where$b^2=c^2-a^2$

Since the hyperbola is having its centre at the $x-$axis, and since the transverse axis is the $x-$axis, it follows that the equation of the hyperbola is of the form $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

From the graph, it can be clearly seen that the vertices of the hyperbola are at $(Â\pm 1,0)$.

Hence, role="math" localid="1648192094034" $a=1$and hence $a^2=1$.

Therefore, the equation of the hyperbola is of the form, role="math" localid="1648192251905" $x^2-\frac{y^2}{b^2}=1$.

Among the given option, only option B is of the form $x^2-\frac{y^2}{b^2}=1$.

Hence, the equation of the hyperbola is$x^2-\frac{y^2}{4}=1$.