Precalculus (6th Edition) Blitzer

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

Chapter 6 - Section 6.3 - Polar Coordinates - Exercise Set - Page 743: 69


The rectangular equation is, ${{\left( x-6 \right)}^{2}}+{{y}^{2}}=36$

Work Step by Step

Using, ${{r}^{2}}={{x}^{2}}+{{y}^{2}}$, we will convert the polar equation to the rectangular equation. Therefore, $\begin{align} & r=12\cos \theta \\ & {{r}^{2}}=12r\cos \theta \\ & {{x}^{2}}+{{y}^{2}}=12r\cos \theta \\ & =12x \end{align}$ We can further simplify it by completing the square on the x as, $\begin{align} & {{x}^{2}}+{{y}^{2}}=12x \\ & {{x}^{2}}+{{y}^{2}}-12x+36=36 \\ & {{\left( x-6 \right)}^{2}}+{{y}^{2}}=36 \end{align}$
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.