The curve in red is the plot of 1+2cos(theta)1+2cos(θ) and the one in purple is the plot of r=1+2cos(theta)r=1+2cos(θ). The purple is drawn from the red. Starting from positive x -ax\isx−axis, the purple curve goes from r=3r=3 at theta = 0θ=0 and decreases until it goes to zero, then decreases further until the minimum r=-1r=−1 at theta = piθ=π, then increases and goes back to zero, and continues increasing until reaching another maximum r=3r=3 at theta = 2*piθ=2⋅π.