Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises - Page 636: 17


$$ \left(\frac{x}{2}\right)^{2}-\left(\frac{y}{\sqrt{12}}\right)^{2}=1. $$

Work Step by Step

Since the foci are $(\pm 4,0)$ and $e=2$, then we have $c=4, e=\frac{c}{a}=\frac{4}{a}=2 $, and hence $a=2 $ and $b=\sqrt{c^2-a^2}=\sqrt{4^2-2^2}=\sqrt{12}$. Hence the equation of the hyperbola is given by $$ \left(\frac{x}{2}\right)^{2}-\left(\frac{y}{\sqrt{12}}\right)^{2}=1. $$
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.