Answer
(a)
Center: $C(0,0)$
Vertices: $V(±2,0)$
Foci: $F(±\sqrt {53},0)$
Asymptotes: $y=±\frac{7}{2}x$
(b)
Length of the transverse axis:
$2a=4$
(c)
Work Step by Step
Hyperbola with center at $(h,k)$ (horizontal transverse axis):
$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$
$\frac{x^2}{4}-\frac{y^2}{49}=1$
$\frac{(x-0)^2}{2^2}-\frac{(y-0)^2}{7^2}=1$
$h=0$
$k=0$
Center: $C(0,0)$
$a=2$
$b=7$
$c^2=a^2+b^2=2^2+7^2=4+49=53$
$c=\sqrt {53}$
Vertices: $V(±a,0)=V(±2,0)$
Foci: $F(±c,0)=F(±\sqrt {53},0)$
Asymptotes: $y=±\frac{b}{a}x=±\frac{7}{2}x$
Length of the transverse axis:
$2a=4$
