Question

convert equation into rectangular coordinates
r=1/(2-cos(theta))

Answer 1

\[r=\frac{1}{2-\cos\theta}~~\iff~~2r-r\cos\theta=1\]
Polar conversions tell you that
\[\begin{cases}x=r\cos\theta\\x^2+y^2=r^2~~\iff~~r=\sqrt{x^2+y^2}\end{cases}\]