Answer
(a) Vertices: $V(0,±4)$
Foci: $F(0,±2\sqrt {26})$,
Asymptotes: $y=±5x$
(b)
Length of the transverse axis:
$2a=20$
(c)
Work Step by Step
$y^2-25x^2=100$
$\frac{y^2}{100}-\frac{x^2}{4}=1$
Hyperbola with vertical transverse axis:
$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
$a^2=100$
$a=10$
$b^2=4$
$b=2$
$c^2=a^2+b^2=100+4=104$
$c=2\sqrt {26}$
(a) Vertices: $V(0,±a)=V(0,±4)$
Foci: $F(0,±c)=F(0,±2\sqrt {26})$,
Asymptotes: $y=±\frac{a}{b}x=±\frac{10}{2}x=±5x$
(b)
Length of the transverse axis:
$2a=20$
