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Parametric representation of a surface

  1. Aug 3, 2009 #1
    1. The problem statement, all variables and given/known data
    Express the surface
    x = 2cos(theta)sin(phi) y=3sin(theta)sin(phi) z=2cos(phi)
    as a level surface f(x,y,z) = 144,
    f(x,y,z) = ?


    2. Relevant equations



    3. The attempt at a solution
    I figured they wanted the equation f(x,y,z) in x^2+y^2+z^2=144 so I though that by making the r's in the equations the same that would be the way to go.--> 24x^2+36y^2+24y^2 = 144 Where am I going wrong???
     
  2. jcsd
  3. Aug 3, 2009 #2

    Dick

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    Looks to me like (x/2)^2+(y/3)^2+(z/2)^2=1. Do you agree? Now how about a form for f(x,y,z)=144?
     
  4. Aug 3, 2009 #3
    How did you know to make the equation into x/2 instead of 2x? Is it really x/r in effect?
     
  5. Aug 3, 2009 #4

    Dick

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    Because I know if x=cos(theta)sin(phi) y=sin(theta)sin(phi) z=cos(phi) then x^2+y^2+z^2=1. I just divided off the constants.
     
  6. Aug 3, 2009 #5
    Oh ok gotcha, great help thanks!
     
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