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    Parametric equations for a Particle Path

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    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

    Please see the attached file.

    Any two dimensional simple curve can be described as a parametric equation of the parameter t
    The general Cartesian equation of a circle of radius R centered around is:
    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:
    It is easy to see that its parametric equations are:
    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.