To determine the equation, apply the formula of hyperbola with vertical transverse axis which is:
Since the center is (0,0), plug-in h=0 and k=0.
To solve for the values of a and b, apply the formula of asymptotes of hyperbola with vertical transverse axis.
Again, plug-in the values of h and k.
Then, substitute `y=+-8/5x` .
To simplify this, divide both sides by x.
So, a=8 and b=5.
Now that the values of a and b are known, plug these to:
Hence, the equation of the hyperbola is `y^2/64-x^2/25=1` .