Chapter 9 Quadratic Relations and Conic Sections - 9.5 Graph and Write Equations of Hyperbolas - 9.5 Exercises - Problem Solving - Page 647: 43a

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From the diagram we can see $a=4\\c=6$ Obtain: $a^2+b^2=c^2\\b^2=c^2-a^2\\b^2=6^2-4^2=20$ The horizontal transverse hyperbola equation: $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ Plug in the given values: $\frac{x^2}{4^2}-\frac{y^2}{20}=1$ Thus, $\frac{x^2}{16}-\frac{y^2}{20}=1$