Answer
Asymptotes: $y=\displaystyle \frac{5}{4}x$ and $y=-\displaystyle \frac{5}{4}x$.
Foci: $(\sqrt{41}, 0)$ and $(-\sqrt{41}, 0)$.
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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$a=4, \quad b=5$
For the foci,
$c^{2}=a^{2}+b^{2}=16+25=41$
$c=\sqrt{41}\approx $6.403
Vertices: $(4,\ 0)$ and $(-4,0)$.
Asymptotes: $y=\displaystyle \frac{5}{4}x$ and $y=-\displaystyle \frac{5}{4}x$.
Foci: $(\sqrt{41}, 0)$ and $(-\sqrt{41}, 0)$.
