Chapter 9 Quadratic Relations and Conic Sections - 9.5 Graph and Write Equations of Hyperbolas - 9.5 Exercises - Skill Practice - Page 645: 16

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Given $$\frac{y^2}{36}-\frac{x^2}{4}=1$$ The denominator of $x^2$ is smaller than $y^2$, so the transverse axis is vertical. Identify the vertices, foci, and asymptotes. Note that $a=6$ and $b=2$. The $x^2-term$ is negative, so the transverse axis is vertical. Find the foci: $c^2=a^2+b^2=6^2+2^2=40\\ \rightarrow c=2\sqrt 10$ The foci are at $(0,\pm 2\sqrt 10)$ The asymptotes are $y=\pm 3x$ Draw the hyperbola.