Precalculus (6th Edition) Blitzer

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

Chapter 6 - Mid-Chapter Check Point - Page 756: 18


The required equation in the polar form is $r=\frac{7}{5\,\cos \,\theta -\sin \,\theta }$.

Work Step by Step

We know that $x=r\,\cos \,\theta \ \text{ and }\ y=r\,\sin \,\theta $. Substitute $x=r\,\cos \,\theta \ \text{ and }\ y=r\,\sin \,\theta $ in the given equation $5x-y=7.$ Therefore, $\begin{align} & 5x-y=7 \\ & 5\left( r\,\cos \,\theta \right)-r\,\sin \,\theta =7 \\ & r\left( 5\,\cos \,\theta -\sin \,\theta \right)=7 \end{align}$ and $r=\frac{7}{5\,\cos \,\theta -\sin \,\theta }$
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