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