Question

Find an equation in standard form for the hyperbola with vertices at (0, ±8) and asymptotes at y equals inverse of plus minus 1 divided by 2x

Answer 1

Using sketch below:
$$\bf

\dfrac{y^2}{a^2}-\dfrac{x^2}{b^2}=1 =(^\star)\\
a=\pm 8\\
\frac{c}{a}=\cos x \implies c=a\cos x\\
b=\sqrt{c^2-a^2}\\
\text{Plug-in values for a,b and c into }(^\star)
$$