Answer
$(B)$
Work Step by Step
The given hyperbola has the $x$-axis as transverse axis; therefore we eliminate $(C)$ and $(D)$. We have to decide between $(A)$ and $(B)$.
The vertices for the given hyperbola are:
$(-1,0),(1,0)$
Check $(1,0)$ in equation $(A)$:
$\dfrac{1^2}{4}-0^2\stackrel{?}{=}1$
$\dfrac{1}{4}\not=1$
So equation $(A)$ does not fit.
Check $(1,0)$ in equation $(B)$:
$1^2-\dfrac{0^2}{4}-0^2\stackrel{?}{=}1$
$1=1\checkmark$
Therefore the correct answer is equation $(B)$.
