Answer
Vertices: $(±\frac{1}{3},0)$
Asymptotes:
$y=±3x~~$ (Black lines)
Work Step by Step
Standard form when transverse axis is horizontal:
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
$9x^2-y^2=1$
$\frac{x^2}{\frac{1}{9}}-\frac{y^2}{1}=1$
$a^2=\frac{1}{9}$
$a=\frac{1}{3}$
$b^2=1$
$b=1$
Vertices when transverse axis is horizontal: $(±a,0)=(±\frac{1}{3},0)$
Asymptotes when transverse axis is horizontal:
$y=±\frac{b}{a}x=±\frac{1}{\frac{1}{3}}x$
$y=±3x$
