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 - Skill Practice - Page 645: 4


See below

Work Step by Step

Rewrite the equation in standard form $$\frac{x^2}{9}-\frac{y^2}{36}=1$$ The denominator of $x^2$ is bigger than $y^2$, so the transverse axis is horizontal. Identify the vertices, foci, and asymptotes. Note that $a=3$ and $b=6$. The $y^2-term$ is positive, so the transverse axis is vertical and the vertices are at $(\pm 3,0)$. Find the foci: $c^2=a^2+b^2=3^2+6^2=45\\ \rightarrow c=3\sqrt 5$ The foci are at $(\pm 3\sqrt 5,0)$ The asymptotes are $y=\pm 2x$ Draw the hyperbola.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.