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: 72


The rectangular equation is, ${{\left( x-4 \right)}^{2}}+{{\left( y-1 \right)}^{2}}=17$

Work Step by Step

Using ${{r}^{2}}={{x}^{2}}+{{y}^{2}}$ we will convert the polar equation to the rectangular equation. Therefore, $\begin{align} & r=8\cos \theta +2\sin \theta \\ & {{r}^{2}}=8r\cos \theta +2r\sin \theta \\ & {{x}^{2}}+{{y}^{2}}=8x+2y \end{align}$ We can further simplify it by completing the square on x and y as, $\begin{align} & {{x}^{2}}+{{y}^{2}}=8x+2y \\ & {{x}^{2}}+{{y}^{2}}-8x-2y+16+1=17 \\ & {{\left( x-4 \right)}^{2}}+{{\left( y-1 \right)}^{2}}=17 \end{align}$
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