# How do you convert 2y - 3x = 2 to polar form?

Aug 25, 2016

$r = \frac{2}{2 \sin \theta - 3 \cos \theta}$

#### Explanation:

To convert from $\textcolor{b l u e}{\text{cartesian to polar form}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{x = r \cos \theta , y = r \sin \theta} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow 2 \left(\textcolor{red}{r \sin \theta}\right) - 3 \left(\textcolor{red}{r \cos \theta}\right) = 2$

$\Rightarrow 2 r \sin \theta - 3 r \cos \theta = 2$

$\Rightarrow r \left(2 \sin \theta - 3 \cos \theta\right) = 2$

$\Rightarrow r = \frac{2}{2 \sin \theta - 3 \cos \theta}$