Answer
(a)
Center: $C(0,0)$
Vertices: $V(0,±2)$
Foci: $F(0,±2\sqrt {5})$
Asymptotes: $y=±\frac{1}{2}x$
(b)
Length of the transverse axis:
$2a=4$
(c)
Work Step by Step
Hyperbola with center at $(h,k)$ (vertical transverse axis):
$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
$x^2-4y^2+16=0$
$x^2-4y^2=-16$
$\frac{y^2}{4}-\frac{x^2}{16}=1$
$\frac{(y-0)^2}{2^2}-\frac{(x-0)^2}{4^2}=1$
$h=0$
$k=0$
Center: $C(0,0)$
$a=2$
$b=4$
$c^2=a^2+b^2=2^2+4^2=4+16=20$
$c=2\sqrt {5}$
Vertices: $V(0,±a)=V(0,±2)$
Foci: $F(0,±c)=F(0,±2\sqrt {5})$,
Asymptotes: $y=±\frac{a}{b}x=±\frac{2}{4}x=±\frac{1}{2}x$
Length of the transverse axis:
$2a=4$
