Answer
Hyperbola
Foci: $( \pm \sqrt 5,0)$
Vertices: $(\pm1,0,)$
Work Step by Step
$4x^2=y^2+4$
$\frac{x^{2}}{1^2}-\frac{y^{2}}{2^2}=1$, the equation of a hyperbola.
$c^{2}=1+4=5$
$c=\sqrt 5$
Foci: $( \pm \sqrt 5,0)$
Vertices: $(\pm1,0,)$