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Sketch the surface of a paraboloid

  1. Jan 24, 2017 #1
    1. The problem statement, all variables and given/known data
    Sketch the surface of a paraboloid z=9-x2 -92 in 3-dimensional xyz-space

    2. Relevant equations

    I assume partial derivatives are involved in some manner

    3. The attempt at a solution

    I attempted to solve by making each variable equal to zero... That didn't work xD. I would appreciate some guidance on how to go about sketching these things in general, many thanks
    Last edited by a moderator: Jan 24, 2017
  2. jcsd
  3. Jan 24, 2017 #2


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    Please correct your statement of the problem. It must be in error.

    What did you get when you set an individual variable to zero ?
  4. Jan 24, 2017 #3
    Y-comp is missing, So it can't be 3d shape.
  5. Jan 24, 2017 #4


    Staff: Mentor

    Do you mean ##z = 9 - x^2 - y^2##?
    Neither ordinary derivatives nor partial derivatives are required in this problem.
    Setting one variable to zero gives you what's called a trace, the intersection of the surface in one of the coordinate planes. For example, assuming the surface is as I wrote it above, setting x = 0, gives you the trace in the y-z plane. Setting y = 0, gives you the trace in the x-z plane.

    There are other techniques that can be used. Your textbook should have some examples, especially for paraboloids. These kinds of surfaces have circular cross-sections along some axis.
  6. Jan 24, 2017 #5
    Yeah there was a mistake on the question paper, I had to email my tutor, 92 goes to y2.

    I'll attempt it again with your advice. Thank you
  7. Jan 24, 2017 #6


    Staff: Mentor

    Look for cross sections in a number of planes that are parallel to the x-y plane.
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