Find the parametric equations for the path of a particle that moves along the circle
x^2 + (y-1)^2 = 4
(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).© BrainMass Inc. brainmass.com June 4, 2020, 2:16 am ad1c9bdddf
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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 ...
The expert examines parametric equation for a particle path.