Answer
Vertices: $(±6,0)$
Asymptotes:
$y=±\frac{1}{3}x~~$ (Black lines)
Work Step by Step
Standard form when transverse axis is horizontal:
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
$4x^2-36y^2=144$
$\frac{x^2}{36}+\frac{y^2}{4}=1$
$a^2=36$
$a=6$
$b^2=4$
$b=2$
Vertices when transverse axis is horizontal: $(±a,0)=(±6,0)$
Asymptotes when transverse axis is horizontal:
$y=±\frac{b}{a}x=±\frac{2}{6}x$
$y=±\frac{1}{3}x$
