Chapter 9 Quadratic Relations and Conic Sections - 9.5 Graph and Write Equations of Hyperbolas - 9.5 Exercises - Problem Solving - Page 646: 39

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We can see that $a=\frac{\sqrt 2}{2}\\c=\frac{\sqrt 3}{2}$ Find b by using the formula: $c^2=a^2+b^2\\b^2=c^2-a^2$ Plug in the given values: $b^2=(\frac{\sqrt 3}{2})^2-(\frac{\sqrt 2}{2})^2\\b=\frac{1}{2}$ The standard form for a horizontal transverse hyperbola is: $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\frac{x^2}{(\frac{\sqrt 2}{2})^2}-\frac{y^2}{(\frac{1}{2})^2}=1\\\frac{x^2}{0.5}-\frac{y^2}{0.25}=1$$