# Parametric equations for a Particle Path

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

x^2 + (y-1)^2 = 4

as follows:

(a) Once around clockwise, starting at (2,1);

(b) Three times around counterclockwise, starting at (2,1);

(c) Halfway around counterclockwise, starting at (0,3).

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#### Solution Preview

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Any two dimensional simple curve can be described as a parametric equation of the parameter t

(1.1)

The general Cartesian equation of a circle of radius R centered around is:

(1.2)

This equation simply tells us that the circle is formed by the set of points that are equally distant from the point , and that distance is R.

If we set and , we get an origin-centered unit circle:

(1.3)

It is easy to see that its parametric equations are:

(1.4)

Where t is the angle measured counterclockwise from the positive x-axis.

If we want to "inflate" the unit circle to radius R, all we have to do is to multiply the x and y coordinates ...

#### Solution Summary

The expert examines parametric equation for a particle path.