Chapter 9 Quadratic Relations and Conic Sections - 9.5 Graph and Write Equations of Hyperbolas - 9.5 Exercises - Skill Practice - Page 645: 25

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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 $c=3\sqrt 6$ and $a=2$. Find $b^2=c^2-a^2=(3\sqrt 6)^2-2^2=50$ $b=50$ Because the transverse axis is horizontal, the standard form of the equation is as follows: $$\frac{x^2}{4}-\frac{y^2}{50}=1$$