Answer
(a)
Vertices: $V(0,±\sqrt 3)$
Foci: $F(0,±2\sqrt {3})$
Asymptotes: $y=±\frac{\sqrt 3}{3}x$
(b)
Length of the transverse axis:
$2a=2\sqrt 3$
(c)
Work Step by Step
$3y^2-x^2-9=0$
$3y^2-x^2=9$
$\frac{y^2}{3}-\frac{x^2}{9}=1$
$\frac{y^2}{(\sqrt 3)^2}-\frac{x^2}{3^2}=1$
Hyperbola with vertical transverse axis:
$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
$a=\sqrt 3$
$b=3$
$c^2=a^2+b^2=(\sqrt 3)^2+3^2=3+9=12$
$c=2\sqrt {3}$
(a)
Vertices: $V(0,±a)=V(0,±\sqrt 3)$
Foci: $F(0,±c)=F(0,±2\sqrt {3})$
Asymptotes: $y=±\frac{a}{b}x=±\frac{\sqrt 3}{3}x$
(b)
Length of the transverse axis:
$2a=2\sqrt 3$
