Chapter 9 Quadratic Relations and Conic Sections - 9.5 Graph and Write Equations of Hyperbolas - 9.5 Exercises - Skill Practice - Page 645: 24

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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 $c=3$ and $a=2\sqrt 2$. Find $b^2=c^2-a^2=3^2-(2\sqrt 2)^2=1$ $b=1$ Because the transverse axis is vertical, the standard form of the equation is as follows: $$\frac{y^2}{8}-\frac{x^2}{1}=1$$