Chapter 9 Quadratic Relations and Conic Sections - 9.5 Graph and Write Equations of Hyperbolas - 9.5 Exercises - Skill Practice - Page 645: 22

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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 5 units from the center, so $c =\pm 10$. The vertices are each 1 unit from the center, so $a=\pm 5\sqrt 3$. Find $b^2=c^2-a^2=10^2-(5\sqrt 3)^2=25$ $b=5$ Because the transverse axis is vertical, the standard form of the equation is as follows: $$\frac{x^2}{75}-\frac{y^2}{25}=1$$