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Cylinders and Quadric Surfaces

  1. Sep 4, 2008 #1
    1. The problem statement, all variables and given/known data

    Consider the equation below.
    x^2 = 3y^2 + 5z^2

    Reduce the equation to one of the standard forms.

    I believe its surface is a cone, but i'm not sure how to get it into the form

    z^2/c^2 = x^2/a^2 + y^2/b^2

  2. jcsd
  3. Sep 5, 2008 #2


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    Your last equation is the standard form for a cone with axis of symmetry along the z axis. Your given equation has axis of symmetry along the x axis and so cannot be put in exactly that form. It can, of course, be put in the form x^2/a^2= y^2/b^2+ z^2/c^2.
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