## Precalculus (6th Edition) Blitzer

The polar equation of $x+5y=8$ that expresses $r$ in terms of $\theta$ is $r=\frac{8}{\left( \cos \theta +5\sin \theta \right)}$.
The relation between polar coordinates and rectangular coordinates can be represented as below: $x=r\cos \theta$ and $y=r\sin \theta$ ……(2) Substitute values of $x\ \text{ and }\ y$ from (2) in (1) to get \begin{align} & x+5y=8 \\ & r\cos \theta +5r\sin \theta =8 \\ & r\left( \cos \theta +5\sin \theta \right)=8 \\ & r=\frac{8}{\left( \cos \theta +5\sin \theta \right)} \end{align} Therefore, the polar equation of $x+5y=8$ that expresses $r$ in terms of $\theta$ is $r=\frac{8}{\left( \cos \theta +5\sin \theta \right)}$.