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?
 A: The line described by your polar equation goes through the origin and is at a constant angle from the $x$ axis.
Now for a line perpendicular to a radial line making a constant angle $\phi$ with the $x$ axis, at a distance $r_0\neq 0$ from the origin, the general polar equation is
$$r(\theta)={r_0\over \cos(\theta-\phi)}$$
A: Hint: Let $x = r \cos \theta$ and $y= r \sin \theta$ and see if you can find the polar equations for
$$y = mx + b \\ y = x + b \\ y = x$$  For the third equation, what do you notice?
A: $\theta=k\pi,k\in\mathbb R$ 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
$$r=-\frac c{a\cos\theta+b\sin\theta}.$$
A: If follows from polar coordinate definition
$$ \theta = constant = c$$
is a line in polar coordinates through the origin. In particular
$$c= 0,  k\pi,\quad k \in \mathbb{R}$$
are lines along x-axis
and
$$c= 1,  \pi(2k-1) $$
are lines along y-axis.
