What is the polar graph of r = 2cos3 (theta) and a characteristic?

we are given the function r=2cos (3θ)

from the pythagorean theorem, r2 = x2 + y2

from the polar definition, x=rcos3θ x/r = cos3θ y=rsin3θ r=2 x/r r2 = 2x x2 + y2 - 2x=0.

This equation represents a parabola