Line in polar coordinates I just wanted to clarify something. A line in polar coordinates has the parameterization of $\theta = k\pi$ for $k \in \mathbb{R}$ right? Or am I missing something?

$\theta=k\pi,k\in\mathbb R$ is just $\theta\in\mathbb R$.
This describes the locus of points at any distance from the origin, in the direction of $\theta$. Hence it is a half-line from the origin, possibly not what you want.

A line of Cartesian equation
$$ax+by+c=0$$ becomes
$$ar\cos\theta+br\sin\theta+c=0$$ or
$$r=-\frac c{a\cos\theta+b\sin\theta}.$$
