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Quadric surfaces

  1. May 20, 2007 #1
    1. The problem statement, all variables and given/known data
    Reduce the equation to one of the standard forms, classify the surface, and sketch it:

    4x = y^2 - 2z^2

    2. Relevant equations

    3. The attempt at a solution
    I really don't know what to do for this one because most of the equations I've seen like this involved x^2.

    Unrelated to this question: For doing these kinds of problems do you find the cross sections on each plane and then sketch it? For example, if the equation is x^2 + 4y^2 + z^2 = 4, you set one variable at a time to k:

    x=k: 4y^2 + z^2 = 4 - k^2
    y=k: x^2 + z^2 = 4 - 4k^2
    z=k: x^2 + 4y^2 = 4 - k^2

    So you can see the cross sections on each plane will be ellipses?

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    2nd problem:

    1. The problem statement, all variables and given/known data
    Find an equation for the surface obtained by rotating the line x = 3y about the x-axis.

    3. The attempt at a solution
    I know this is a cone about the x-axis, but not sure how to get the exact equation.
     
    Last edited: May 20, 2007
  2. jcsd
  3. May 20, 2007 #2

    D H

    User Avatar
    Staff Emeritus
    Science Advisor


    So change the names of the variables.

    Look at it this way: The standard form for a parabola is y=ax^2+bx+c. x=ay^2+by+c is also a parabola.
     
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