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How to Find Access of Symmetry in Quadric Surface?

  1. Jan 28, 2012 #1
    1. The problem statement, all variables and given/known data
    Construct a hyperboloid of one sheet whose axis of symmetry is the y-axis.

    2. Relevant equations

    Hyperboloid of One Sheet --> x^2 + y^2 - z^2 = c

    3. The attempt at a solution

    The relevant equation is the one given in the book and in my notes. Obviously I can have this shape in other axes. I know that I am supposed to try and visualise the shapes in 3space, but it's a skill that I find very difficult to grasp.

    In the above equation, I've got in:
    x/y plane: circle
    x/z plane: hyperbola
    y/z plane: hyperbola

    I'm unsure how to determine the axis of rotation and would be grateful for any help in visualising the shape.
  2. jcsd
  3. Jan 28, 2012 #2


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    Well, you have noticed the trace in the z=0 plane is a circle. Or is it? Does it matter if c > 0 or not? But anyway, what about traces in z = constant planes other than the xy plane. You will get circles, or nothing, depending on the relative size of z and c and whether the hyperboloid has one or two sheets. But, to answer your question, the axis that gives the centers of the circular cross sections is the axis of rotation.
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