Chapter 9 Quadratic Relations and Conic Sections - 9.5 Graph and Write Equations of Hyperbolas - 9.5 Exercises - Problem Solving - Page 646: 38

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Find b by using the formula: $c^2=a^2+b^2\\b^2=c^2-a^2$ Plug in the given values: $b^2=33^2-56^2\\b=\sqrt 2047$ The standard form for a horizontal transverse hyperbola is: $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\frac{x^2}{33^2}-\frac{y^2}{(\sqrt 2047)^2}=1\\\frac{x^2}{1089}-\frac{y^2}{2047}=1$$