Answer
(a)
Center: $C(0,0)$
Vertices: $V(±4,0)$
Foci: $F(±2\sqrt {6},0)$
Asymptotes: $y=±\frac{1}{\sqrt 2}x$
(b)
Work Step by Step
Hyperbola with center at $(h,k)$ (horizontal transverse axis):
$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$
$x^2-2y^2=16$
$\frac{x^2}{16}-\frac{y^2}{8}=1$
$\frac{(x-0)^2}{4^2}-\frac{(y-0)^2}{(2\sqrt 2)^2}=1$
$h=0$
$k=0$
Center: $C(0,0)$
$a=4$
$b=2\sqrt 2$
$c^2=a^2+b^2=4^2+(2\sqrt 2)^2=16+8=24$
$c=2\sqrt {6}$
Vertices: $V(±a,0)=V(±4,0)$
Foci: $F(±c,0)=F(±2\sqrt {6},0)$
Asymptotes: $y=±\frac{b}{a}x=±\frac{2\sqrt 2}{4}x=±\frac{1}{\sqrt 2}x$
