I am trying to convert $(x - 1)^2 - y^2 = 1$ to polar form.
I expanded the binomial, simplified, and got $x^2 - y^2 - 2x = 0$.
Then I replaced $x$ with $r\cos(\theta)$ and $y$ with $r\sin(\theta)$.
After squaring, I factored out the $r^2$, and replaced $\sin^{2}(\theta) - \cos^{2}(\theta)$ with $\cos(2\theta)$.
Solving for $r$, I ended up with $r= (2\cos(\theta))/\cos(2\theta)$.
Is there any other ways to do this without using eccentricities?