Answer
(a)
Vertices: $V(0,±3)$
Foci: $F(0,±\sqrt {34})$
Asymptotes: $y=±\frac{3}{5}x$
(b)
Length of the transverse axis:
$2a=6$
(c)
Work Step by Step
$25y^2-9x^2=225$
$\frac{y^2}{9}-\frac{x^2}{25}=1$
$\frac{y^2}{3^2}-\frac{x^2}{5^2}=1$
Hyperbola with vertical transverse axis:
$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
$a=3$
$b=5$
$c^2=a^2+b^2=3^2+5^2=9+25=34$
$c=\sqrt {34}$
(a)
Vertices: $V(0,±a)=V(0,±3)$
Foci: $F(0,±c)=F(0,±\sqrt {34})$
Asymptotes: $y=±\frac{a}{b}x=±\frac{3}{5}x$
(b)
Length of the transverse axis:
$2a=6$
