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Surfaces of 3 Variable Question

  1. Sep 14, 2011 #1
    1. The problem statement, all variables and given/known data

    A cone C, with height I and radius I, has its base in
    the xz-plane and its vertex on the positive y-axis. Find a
    function g(x, y, z) such that C is part of the level surface
    g(x, y, z) = 0.

    2. Relevant equations
    What would be the formula for the cone such that the base of the cone is lying on the xz-plane and the vertex is on the y-axis?


    3. The attempt at a solution
    We know that the formula for a cone is [tex]x^2+y^2-z^2[/tex], but we don't know where to go from there to get the formula for the description above.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 14, 2011 #2

    Dick

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    Science Advisor
    Homework Helper

    x^2+y^2-z^2 has it's vertex at (0,0,0) and it's axis along the z axis. Your cone has it's vertex at (0,I,0) and axis along the y axis. You'll need to interchange some variables to get the axis right and then shift the vertex up to (0,I,0). Sketch some graphs.
     
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