Answer
(a)
Center: $C(0,0)$
Vertices: $V(0,±1)$
Foci: $F(0,±5)$
Asymptotes: $y=±\frac{4}{3}x$
(b)
Length of the transverse axis:
$2a=8$
(c)
Work Step by Step
Hyperbola with center at $(h,k)$ (vertical transverse axis):
$\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1$
$-\frac{x^2}{9}+\frac{y^2}{16}=1$
$\frac{(y-0)^2}{4^2}-\frac{(x-0)^2}{3^2}=1$
$h=0$
$k=0$
Center: $C(0,0)$
$a=4$
$b=3$
$c^2=a^2+b^2=4^2+3^2=16+9=25$
$c=5$
(a) Vertices: $V(0,±a)=V(0,±1)$
Foci: $F(0,±c)=F(0,±5)$,
Asymptotes: $y=±\frac{a}{b}x=±\frac{4}{3}x$
(b)
Length of the transverse axis:
$2a=8$
