Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

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: 9

Answer

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Work Step by Step

Given: $12y^2-20x^2=240$ $$\frac{y^2}{20}-\frac{x^2}{12}=1$$ The denominator of $x^2$ is greater than $y^2$, so the transverse axis is vertical. Identify the vertices, foci, and asymptotes. Note that $a=2\sqrt 5$ and $b=2\sqrt 3$. The $x^2-term$ is negative, so the transverse axis is vertical and the vertices are at $(0,2\pm 5)$. Find the foci: $c^2=a^2+b^2=(2\sqrt 5)^2+(2\sqrt 3)^2=32\\ \rightarrow c=4\sqrt 2$ The foci are at $(0,\pm 4\sqrt 2)$ The asymptotes are $y=\pm \sqrt \frac{5}{3}x$ Draw the hyperbola.
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