Answer
(a) Vertices: $(0,±6)$
Foci: $(0,±\sqrt {42})$
Asymptotes:
$y=±3x~~$ (Black lines)
(b) Length of the transverse axis:
$2a=12$
Work Step by Step
Hyperbola with vertical transverse axis:
$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
$\frac{y^2}{36}-\frac{x^2}{4}=1$
$a^2=36$
$a=6$
Vertices: $(0,±a)=(0,±6)$
$b^2=4$
$b=2$
$c^2=a^2+b^2=36+6=42$
$c=\sqrt {42}$
Foci: $(0,±c)=(0,±\sqrt {42})$
Asymptotes:
$y=±\frac{a}{b}x$
$y=±\frac{6}{2}x=±3x$
Length of the transverse axis:
$2a=12$
