Answer
(a) Vertices: $(±2,0)$
Foci: $(±2\sqrt 5,0)$
Asymptotes:
$y=±2x~~$ (Black lines)
(b) Length of the tranverse axis:
$2a=4$
Work Step by Step
Hyperbola with horizontal transverse axis:
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
$\frac{x^2}{4}-\frac{y^2}{16}=1$
$a^2=4$
$a=2$
Vertices: $(±a,0)=(±2,0)$
$b^2=16$
$b=4$
$c^2=a^2+b^2=4+16=20$
$c=2\sqrt 5$
Foci: $(±c,0)=(±2\sqrt 5,0)$
Asymptotes:
$y=±\frac{b}{a}x$
$y=±\frac{4}{2}x=±2x$
Length of the transverse axis:
$2a=4$
