Chapter 9 Quadratic Relations and Conic Sections - 9.5 Graph and Write Equations of Hyperbolas - 9.5 Exercises - Skill Practice - Page 645: 23

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The foci and vertices lie on the y-axis equidistant from the origin, so the transverse axis is vertical and the center is the origin. The foci are $c =4\sqrt 5$ and $a=4$. Find $b^2=c^2-a^2=(4\sqrt 5)^2-4^2=64$ $b=8$ Because the transverse axis is vertical, the standard form of the equation is as follows: $$\frac{y^2}{16}-\frac{x^2}{64}=1$$