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