Answer
(a) Vertices: $(0,±3)$
Foci: $(0,±5)$
Asymptotes:
$y=±\frac{3}{4}x~~$ (Black lines)
(b) Length of the transverse axis:
$2a=6$
Work Step by Step
Hyperbola with vertical transverse axis:
$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
$\frac{y^2}{9}-\frac{x^2}{16}=1$
$a^2=9$
$a=3$
Vertices: $(0,±a)=(0,±3)$
$b^2=16$
$b=4$
$c^2=a^2+b^2=9+16=25$
$c=5$
Foci: $(0,±c)=(0,±5)$
Asymptotes:
$y=±\frac{a}{b}x$
$y=±\frac{3}{4}x$
Length of the transverse axis:
$2a=6$
