Sketch the curves given by the parametric equation

Question

Sketch the curves given by the following parametric equations (find corresponding Cartesian equations if possible).

(a) In R², x = 1 + cos t, y = 2 + sin t, t ?[0, p]. Mark the points corresponding to t = 0, p/2, pon your sketch.

(b) In R², x = 1 + 2 cos t, y = 2 + sin t, t ?[0, 2p]. Mark the points corresponding to t = 0, p/2, p, 3 p /2, 2 pon your sketch.

(c) In R², x = 2t, y = 4t²+ 1, t ?[0, 1]. Mark the points corresponding to t = 0, 1/2, 1.

(d) In R³, x = 0, y = 3-3t, z = 2t, t ?R. Mark the points corresponding to t = 0, 1, -1.