Convert $$$2 x + 3 y = 6$$$ to polar coordinates

Convert $$$2 x + 3 y = 6$$$ to polar coordinates.

In polar coordinates, $$$x = r \cos{\left(\theta \right)}$$$ and $$$y = r \sin{\left(\theta \right)}$$$.

Thus, the input can be rewritten as $$$3 r \sin{\left(\theta \right)} + 2 r \cos{\left(\theta \right)} = 6$$$.

Simplify: the input now takes the form $$$3 r \sin{\left(\theta \right)} + 2 r \cos{\left(\theta \right)} - 6 = 0$$$.

Thus, $$$r = \frac{6}{3 \sin{\left(\theta \right)} + 2 \cos{\left(\theta \right)}}$$$.

$$$2 x + 3 y = 6$$$A in polar coordinates is $$$r = \frac{6}{3 \sin{\left(\theta \right)} + 2 \cos{\left(\theta \right)}}$$$A.