Answer
(a)
Center: $C(0,0)$
Vertices: $V(±7,0)$
Foci: $F(±9,0)$
Asymptotes: $y=±\frac{4\sqrt 2}{7}x$
(b)
Length of the transverse axis:
$2a=14$
(c)
Work Step by Step
Hyperbola with center at $(h,k)$ (horizontal transverse axis):
$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$
$\frac{x^2}{49}-\frac{y^2}{32}=1$
$\frac{(x-0)^2}{7^2}-\frac{(y-0)^2}{(4\sqrt 2)^2}=1$
$h=0$
$k=0$
Center: $C(0,0)$
$a=7$
$b=4\sqrt 2$
$c^2=a^2+b^2=7^2+(4\sqrt 2)^2=49+32=81$
$c=9$
Vertices: $V(±a,0)=V(±7,0)$
Foci: $F(±c,0)=F(±9,0)$
Asymptotes: $y=±\frac{b}{a}x=±\frac{4\sqrt 2}{7}x$
Length of the transverse axis:
$2a=14$
