1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to Find Access of Symmetry in Quadric Surface?
  1. Quadric surfaces (Replies: 1)

Loading...