Answer
(a) Vertices: $V(±a,0)=V(±3,0)$
Foci: $F(±c,0)=F(±\sqrt {73},0)$,
Asymptotes: $y=±\frac{b}{a}x=±\frac{8}{3}x$
(b)
Length of the transverse axis:
$2a=6$
(c)
Work Step by Step
$\frac{x^2}{9}-\frac{y^2}{64}=1$
Hyperbola with horizontal transverse axis:
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
$a^2=9$
$a=3$
$b^2=64$
$b=8$
$c^2=a^2+b^2=9+64=73$
$c=\sqrt {73}$
(a) Vertices: $V(±a,0)=V(±3,0)$
Foci: $F(±c,0)=F(±\sqrt {73},0)$,
Asymptotes: $y=±\frac{b}{a}x=±\frac{8}{3}x$
(b)
Length of the transverse axis:
$2a=6$
