Chapter 9 Quadratic Relations and Conic Sections - 9.5 Graph and Write Equations of Hyperbolas - 9.5 Exercises - Skill Practice - Page 645: 19

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The foci and vertices lie on the x-axis equidistant from the origin, so the transverse axis is horizontal and the center is the origin. The foci are each 6 units from the center, so $c =6$. The vertices are each 2 units from the center, so $a=2 $. Find $b^2=c^2-a^2=6^2-2^2=32$ $b=\sqrt 32$ Because the transverse axis is vertical, the standard form of the equation is as follows: $$\frac{x^2}{4}-\frac{y^2}{32}=1$$