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