Answer
$(A)$
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:
$(-2,0),(2,0)$
Check $(2,0)$ in equation $(A)$:
$\dfrac{2^2}{4}-0^2\stackrel{?}{=}1$
$1=1\checkmark$
So equation $(A)$ fits.
Check $(2,0)$ in equation $(B)$:
$2^2-\dfrac{0^2}{4}\stackrel{?}{=}1$
$4\not=1$
So equation $(B)$ doesn't fit.
Therefore, the correct answer is equation $(A)$.
