Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.9 - The Coordinate Plane; Graphs of Equations; Circles - 1.9 Exercises - Page 104: 107

Answer

The given equation is symmetric about the origin.

Work Step by Step

$x^{2}y^{2}+xy=1$ Test for symmetry about the $y$-axis by substituting $x$ by $-x$ and simplifying: $(-x)^{2}y^{2}+(-x)y=1$ $x^{2}y^{2}-xy=1$ Since substituting $x$ by $-x$ does not yield an equivalent equation, the equation is not symmetric about the $y$-axis. Test for symmetry about the $x$-axis by substituting $y$ by $-y$ and simplifying: $x^{2}(-y)^{2}+x(-y)=1$ $x^{2}y^{2}-xy=1$ Since substituting $y$ by $-y$ does not yield an equivalent equation, the equation is not symmetric about the $x$-axis. Test for symmetry about the origin by substituting $x$ by $-x$ and $y$ by $-y$ and simplifying: $(-x)^{2}(-y)^{2}+(-x)(-y)=1$ $x^{2}y^{2}+xy=1$ Since substituting $x$ by $-x$ and $y$ by $-y$ yields an equivalent equation, the equation is symmetric about the origin.
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.