The ellipse X² and y(t) = + = 1 can be drawn with parametric equations where x(t) is written in the form x(t) = rcos (t) with r =

x=5+e(2t) y=1-e(t)

Find parametric equations for the path of a particle that moves along the circle  x2 + (y − 1)2 = 4  in the manner described. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.) (a) Once around clockwise, starting at (2, 1).  0 ≤ t ≤ 2?. (b) Four times around counterclockwise, starting at (2, 1).  0 ≤ t ≤ 8?. (c) Halfway around counterclockwise, starting at (0, 3).  0 ≤ t ≤ ?.

Write a set of parametric equations for the ellipse which begins at the point (3, 0) at time t = 0, then passes through (1, 4) at time t = " (-1, 0) at time t = ", (1. -4) at time t= before returning to (3, 0) at time t= Note: The answers should be functions of t x(t)= y(t)=