In converting from polar to cartesian coordinates, the following equations are useful:
r = √(x2 + y2)
x = r*cos(θ)
y = r*sin(θ)
We can multiply both sides of your equation by the denominator to yield
r[1 - cos(θ)] = 2. Distributing, we have
r - r*cos(θ) = 2. Convert from polar to cartesian by making appropriate substitutions:
√(x2 + y2) - x = 2. Add x to both sides:
√(x2 + y2) = x + 2. Square both sides:
x2 + y2 = x2 + 4x + 4. Subtract x2 from both sides:
y2 = 4x + 4. Solve for x:
x = y2/4 - 1.
This is a parabola whose line of symmetry is the x-axis.