Answer
Hyperbola matches with the graph labeled as II
Work Step by Step
$16y^2-x^2=144$
$\frac{y^2}{9}-\frac{x^2}{144}=1$
Hyperbola with vertical transverse axis:
$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
So:
$a^2=9$
$a=3$
Vertices: $V(0,±a)=V(0,±3)$
Hyperbola matches with the graph labeled as II
