Chapter 9 Quadratic Relations and Conic Sections - 9.5 Graph and Write Equations of Hyperbolas - 9.5 Exercises - Quiz for Lessons 9.4-9.5 - Page 648: 7

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Given: $$\frac{y^2}{25}-\frac{x^2}{64}=1$$ The denominator of $x^2$ is greater than $y^2$, so the transverse axis is vertical. Identify the vertices, foci, and asymptotes. Note that $a=5$ and $b=8$. The $x^2-term$ is negative, so the transverse axis is vertical and the vertices are at $(0,\pm 5)$. Find the foci: $c^2=a^2+b^2=5^2+8^2=89\\ \rightarrow c=\sqrt 89$ The foci are at $(0,\pm \sqrt 89)$ The asymptotes are $y=\pm \frac{5}{8}x$ Draw the hyperbola.