A simplified model assumes that the orbits of Earth and Mars are circular with radii of 2 and 3, respectively, and that Earth completes one orbit in one year while Mars takes two years. When t = 0, Earth is at (2, 0) and Mars is at (3, 0); both orbit the Sun (at (0, 0)) in the counterclockwise direction. The position of Mars relative to Earth is given by the parametric equations 

x = (3 - 4 cos πt) cos πt + 2, y = (3 - 4 cos πt) sin πt.

a. Graph the parametric equations, for 0 ≤ t ≤ 2.

b. Letting r = (3 - 4 cos πt), explain why the path of Mars relative to Earth is a limaçon.