Answer
Asymptotes: $y=\displaystyle \pm\frac{4}{5}x .$
Foci: $(2\sqrt{41}, 0)$ and $(-2\sqrt{41}, 0)$.
Work Step by Step
The hyperbola
$\displaystyle \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$
has a horizontal transverse axis and two asymptotes
$y=\displaystyle \frac{b}{a}x$ and $y=-\displaystyle \frac{b}{a}x$.
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$a=10, \quad b=8$
For the foci,
$c^{2}=a^{2}+b^{2}=100+64=164$
$ c=2\sqrt{41}\approx$12.806
Vertices: $(10,\ 0)$ and $(-10,0)$.
Asymptotes: $y=\displaystyle \pm\frac{8}{10}x =\displaystyle \pm\frac{4}{5}x .$
Foci: $(2\sqrt{41}, 0)$ and $(-2\sqrt{41}, 0)$.