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Write the equation in standard form of the hyperbola with center at the origin, its transverse axis is vertical, and it's asymptotes are y=+/- (8/5)x

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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` .

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