Answer
(a)
Vertices: $V(0,±2)$
Foci: $F(0,±2\sqrt {2})$
Asymptotes: $y=±x$
(b)
Length of the transverse axis:
$2a=4$
(c)
Work Step by Step
$x^2-y^2+4=0$
$x^2-y^2=-4~~$ (Multiply both sides by $-1$)
$y^2-x^2=4$
$\frac{y^2}{4}-\frac{x^2}{4}=1$
$\frac{y^2}{2^2}-\frac{x^2}{2^2}=1$
Hyperbola with vertical transverse axis:
$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
$a=2$
$b=2$
$c^2=a^2+b^2=2^2+2^2=4+4=8$
$c=2\sqrt {2}$
(a)
Vertices: $V(0,±a)=V(0,±2)$
Foci: $F(0,±c)=F(0,±2\sqrt {2})$
Asymptotes: $y=±\frac{a}{b}x=±\frac{2}{2}x=±x$
(b)
Length of the transverse axis:
$2a=4$
