Answer
Asymptotes: $y=\displaystyle \pm\frac{5}{8}x$
Foci: $(0, \sqrt{89})$ and $(0, -\sqrt{89})$.
Work Step by Step
The hyperbola $\displaystyle \frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1$
has a vertical transverse axis and two asymptotes
$y=\displaystyle \pm\frac{a}{b}x$
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$a=5, \quad b=8$
For the foci,
$c^{2}=a^{2}+b^{2}=25+64=89$
$c=\sqrt{89} \approx 9.434$
Vertices:$(0,5)$ and $(0, -5)$
Asymptotes:
$y=\displaystyle \pm\frac{a}{b}x=\pm\frac{5}{8}x$
Foci:$(0, \sqrt{89})$ and $(0, -\sqrt{89})$.
