anonymous
  • anonymous
Write the parameterization, in the xy-plane, of a particle traveling once around a circle with its center at (1,2) and a radius of 5 traveling clockwise starting from the point (6,2).
Mathematics
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SOLVED
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katieb
  • katieb
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eyust707
  • eyust707
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eyust707
  • eyust707
I am a bit rusty with these but heres my stab at it: a circle centered at the origin we would get: \[x^2 + y^2 = r^2 \] where \[r = 5\] so centered at the origin we would get the equaiton: \[x^2+y^2=25\] but we want to translate over one and up two: \[(x-1)^2+(y-2)^2=25\] by looking at the unit circle and the properties of sin and cos we notice that \[x=rsin(t)\] \[y=rcos(t)\] I believe you can just sub these in for x and y. If you notice when t goes from 0 to 2pi you will have drawn the exact circle you want
eyust707
  • eyust707
\[(5\sin(t)-1)^2+(5\cos(t)-2)^2=25 \rightarrow 0 \le t \le2\pi \]

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eyust707
  • eyust707
im not 100 percent sure tho
eyust707
  • eyust707
hmm i dunno about that answer.. it doesnt graph well on wolfram alpha =/

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