Final answer:
The parametric equations for the clockwise motion around the given circle, starting at the point (3, 2), are x(t) = 3 sin(t) and y(t) = 2 + 3 cos(t), where the circle has a radius of 3 and is centered at the point (0, 2).
Step-by-step explanation:
The question asks for parametric equations for the path of a particle that moves around a given circle clockwise, starting at the point (3, 2). Given that the standard equation for a circle in parametric form is x = h + r cos(θ) and y = k + r sin(θ), where (h, k) is the center of the circle, r is the radius, and θ represents the angle parameter.
To create parametric equations for the given circle x² (y - 2)² = 9, we notice that it can be rewritten as (x/3)² + ((y - 2)/3)² = 1, which is a circle of radius 3 centered at (0, 2). The parametric equations for a counterclockwise path around the circle with radius 3 and center at (0, 2) are x(t) = 3 cos(t) and y(t) = 2 + 3 sin(t).
However, since we need to move clockwise and start at (3, 2), we have to adjust the angle by π/2 to start at the correct position and reverse the direction of motion. Hence, the parametric equations would be x(t) = 3 cos(t - π/2) and y(t) = 2 + 3 sin(t - π/2), or simplified x(t) = 3 sin(t), y(t) = 2 + 3 cos(t), where t is the parameter.