Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 13 - Conic Sections - 13.3 Conic Sections: Hyperbolas - 13.3 Exercise Set - Page 871: 44

Answer

Ellipse

Work Step by Step

$56{{x}^{2}}-17{{y}^{2}}=234-13{{x}^{2}}-38{{y}^{2}}$ Combine like terms: $56{{x}^{2}}+13{{x}^{2}}-17{{y}^{2}}+38{{y}^{2}}-234=0$ $69{{x}^{2}}+21{{y}^{2}}-568=0$ Compare the equation $69{{x}^{2}}+21{{y}^{2}}-568=0$ with the standard equation of a conic section $A{{x}^{2}}+B{{y}^{2}}+Cxy+Dx+Ey+F=0$, Here, $A=69,B=21$ Here, A and B have the same sign, but $ A \ne B $. Therefore, the graph of the equation is an ellipse.
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.