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Homework Help: Sketch the surface

  1. Jan 15, 2010 #1
    1. The problem statement, all variables and given/known data
    Sketch the surface x+y2+z2+1=0


    2. Relevant equations



    3. The attempt at a solution
    I'm not to sure how to proceed with this. My initial idea was to re-arrange for x such that
    x=-1-y2+z2=-1-r2

    thus the equation for the surface becomes y2+z2=r2

    I'm not sure what to do next though.
     
  2. jcsd
  3. Jan 15, 2010 #2

    benorin

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    [itex]x=y^2+z^2[/itex] is a bowl opening which direction?
    [itex]x=1+y^2+z^2[/itex] is the same bowl shifted one unit in which direction?
    [itex]x=-(1+y^2+z^2)=-1-y^2-z^2[/itex] is the second bowl reflected about which axis?
     
  4. Jan 15, 2010 #3
    okay x=y2+z2 is a bowl opening in the x direction
    x=1+y2+z2 is the same bowl shifted by 1 unit to the right along the x-axis

    x=-1-y2-z2 is the same bowl reflected along the negative x-axis.

    So the image should be a bowl that runs along the positive and negative x-axis.
     
  5. Jan 15, 2010 #4

    benorin

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    no picture? :(
     
  6. Jan 15, 2010 #5
    heres the picture I drew, I wasn't quite sure whether to draw the two bowls as connected or seperated object

    http://img62.imageshack.us/img62/465/cci1501201000000.jpg [Broken]
     
    Last edited by a moderator: May 4, 2017
  7. Jan 15, 2010 #6

    benorin

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    [itex]x=-(1+y^2+z^2)\le -1[/itex] right?
     
  8. Jan 15, 2010 #7
    ah, so then the bowl only runs along the negative x axis like this
    http://img25.imageshack.us/img25/465/cci1501201000000.jpg [Broken]
     
    Last edited by a moderator: May 4, 2017
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