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 - 2)^2 = 9 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 (3, 2). 0 Less than or equal to t Less than or equal to 2 Pi . (b) Three times around counterclockwise, starting at (3, 2). 0 Less than or equal to t Less than or equal to 6 Pi. (c) Halfway around counterclockwise, starting at (0, 5). 0 Less than or equal to t Less than or equal to Pi.

Explanation / Answer

the centre of the circle is (0,2), r =3
Point (3,2) are the far right on the circle while (0,5) 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 6?
c) the path is (2cos (?+?/2),1 +2sin( ?+?/2)) for ? = 0 to ?
which is (-2sin(?) , 1+ 2cos(?))for ? = 0 to ?

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