Chapter 9 Quadratic Relations and Conic Sections - 9.5 Graph and Write Equations of Hyperbolas - 9.5 Exercises - Skill Practice - Page 646: 29

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Given $48x^2+12y^2=48$ Rewrite the equation in standard form $$\frac{x^2}{1}+\frac{y^2}{4}=1$$ The denominator of $x^2$ is smaller than $y^2$, so the transverse axis is vertical. Identify the vertices, foci, and asymptotes. Note that $a=1$ and $b=2$. The $x^2-term$ is negative, so the transverse axis is vertical and the vertices are at $(0,\pm 1)$. Draw the hyperbola.