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Parametric curve

  1. Oct 25, 2009 #1
    1. The problem statement, all variables and given/known data
    Find parameterizations for the circle of radius 3 about the point (3,4)


    2. Relevant equations



    3. The attempt at a solution

    The circle of radius 3 about the origin looks like cos2t + sin2t = 3

    But I can't figure out how to parameterize it around (3,4), any advice?
     
  2. jcsd
  3. Oct 25, 2009 #2

    Office_Shredder

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    If you have a circle around the origin, and you want to move it so that it's a circle around the point (3,4) what vector do you have to add to your circle? Think about it in terms of transformations on the plane. Hint: You want the center of the circle around the origin to move to the center of the circle around (3,4)
     
  4. Oct 25, 2009 #3
    the circle will be (x-3)2+(y-4)2 = 9, but how do I parameterize that?
     
  5. Oct 26, 2009 #4

    HallsofIvy

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    Use the fact that [itex]sin^2 t+ cos^2 t= 1[/itex] for all t.
     
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