Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.4 - Graphs of Polar Equations - Concept and Vocabulary Check - Page 753: 7


The graphs of $r=a+b\sin \theta $, $r=a-b\sin \theta $, $r=a+b\cos \theta $, and $r=a-b\cos \theta $, $a>0$, $n>0$, are called limaçons, a French word for snail. The ratio $\frac{a}{b}$ determines the graph’s shape. If, $\frac{a}{b}=1$, the graph is shaped like a heart and called a cardioid. If $\frac{a}{b}<1$, the graph has an inner loop.

Work Step by Step

For the graph of the given function $r=a+b\sin \theta $, $r=a-b\sin \theta $, $r=a+b\cos \theta $, and $r=a-b\cos \theta $, $a>0$, $n>0$, the ratio of $\frac{a}{b}$ determines the shape of the graph. As the ratio of $\frac{a}{b}$ changes from zero to one, the graph changes it shape from an inner loop to a cardioid and as the ratio of $\frac{a}{b}$ increases beyond one, the shape of the graph is converted into a snail-like shape.
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.