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