Find parametric equations for the path of a particle that moves along the circle

Question

Find parametric equations for the path of a particle that moves along the circle x^2 + (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.) Once around clockwise, starting at (2, 1). 0 lessthanorequalto t lessthanorequalto 2 pi. Four times around counterclockwise, starting at (2, 1). 0 lessthanorequalto t lessthanorequalto 8 pi Halfway around counterclockwise, starting at (0, 3). 0 lessthanorequalto t lessthanorequalto pi.

Explanation / Answer

The centre of the circle is (0, 1), r =2

Point (2, 1) are the far right on the circle while (0,3) is the highest point on the circle.

X = rcos +cx = 2cos, y = rsin+cy =2sin+1

a) The path is (2cos (-), 2sin (-) +1) which is (2cos , 1-2sin ) for = 0 to 2

b) the path is (2cos ,1 +2sin ) for = 0 to 8

c) The path is (2cos (+/2),1 +2sin( +/2)) for = 0 to

Which is (-2sin (), 1+ 2cos ()) for = 0 to

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