Aclown is juggling at a circus. the path of the ball is given by the parametric equations x=2cos t+2 and y=3sin t+3. in what direction is the ball moving? -up and to the right -counterclockwise -down and to the right -clockwise

We need to find the direction the ball is moving, so wee have this parametric equation, namely:


Note that this parametric equation is an ellipse. The graph of this equation is given in figure below. So, we well substitute some values of t in the equation:

If t = 0
x = 4 and y = 3
P0(4, 3)

if t = 1
x = 3.08 and y = 5.52
P1(3.08, 5.52)

if t = 2
x = 1.16 and y = 5.72
P2(1.16, 5.72)

Finally, as shown in the figure, the answer is B. counterclockwise. Notice the trajectory that follows P0, P1 and P2.