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Math Help - Find Parametric Equation for Moving Particle

  1. #1
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    Find Parametric Equation for Moving Particle

    Hello. I am familiar with parametric equations but the way this one is being asked is throwing me off.

    Find parametric equations for the path of a particle that moves along the circle
    (x-1)^2 + (y+2)^2 = 4 three times clockwise, starting at point (1,-4).
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lindsmitch View Post
    Hello. I am familiar with parametric equations but the way this one is being asked is throwing me off.

    Find parametric equations for the path of a particle that moves along the circle
    (x-1)^2 + (y+2)^2 = 4 three times clockwise, starting at point (1,-4).
    i assume you know the (counter-clockwise) way to parameterize a circle, just do it the other way. you then want to choose the angle so that you get 3 revolutions out of it, beginning at the indicated point. How's that?
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  3. #3
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    Hello, lindsmitch!

    \text{Find parametric equations for the path of a particle}
    \text{that moves along the circle: }\:(x-1)^2 + (y+2)^2 \:=\: 4
    \text{ three times clockwise, starting at point (1, -4)}

    The path is a circle, center (1,-2) and radius 2.
    The curve starts at "6 o'clock" and moves clockwise for 3 revolutions.


    There is a variety of ways to write the parametric equations.
    . . I'll use the easiest way (for me).


    . . \begin{Bmatrix}{x &=& 1 + 2\cos\theta \\ y &=& \text{-}2 + 2\sin\theta \end{Bmatrix}\quad \text{ for }\,\theta = \frac{3\pi}{2}\,\text{ to }\,\theta = \text{-}\frac{9\pi}{2}
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  4. #4
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    Thank you both very much. That was very helpful.

    In the future, how would I have arrived at those parametric equations Soroban? Did you just use the conversion x = r * cos(theta) and y = r*sin(theta)?
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