Answer
(a)
Center: $C(0,0)$
Vertices: $V(0,±5)$
Foci: $F(0,±\sqrt {29})$
Asymptotes: $y=±\frac{5}{2}x$
(b)
Length of the transverse axis:
$2a=10$
(c)
Work Step by Step
Hyperbola with center at $(h,k)$ (vertical transverse axis):
$\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1$
$\frac{y^2}{25}-\frac{x^2}{4}=1$
$\frac{(y-0)^2}{5^2}-\frac{(x-0)^2}{2^2}=1$
$h=0$
$k=0$
Center: $C(0,0)$
$a=5$
$b=2$
$c^2=a^2+b^2=5^2+2^2=25+4=29$
$c=\sqrt {29}$
Vertices: $V(0,±a)=V(0,±5)$
Foci: $F(0,±c)=F(0,±\sqrt {29})$
Asymptotes: $y=±\frac{a}{b}x=±\frac{5}{2}x$
Length of the transverse axis:
$2a=10$
