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Homework Help: Parametric equations for a hyperbolic paraboloid

  1. Sep 15, 2005 #1
    I need to find a set of parametric equations for a hyperbolic paraboloid. The hint is that I should review some trigonometric identities that involve differences of squares that equal 1.

    The equation is:
    [tex]
    \frac{y^2}{2}- \frac{x^2}{4} - \frac{z^2}{9} = 1
    [/tex]

    And what I have is

    [tex]
    y= \sqrt{2}*sec(t)*sec(s)
    [/tex]
    [tex]
    x=2*tan(t)*sec(s)
    [/tex]
    [tex]
    z=3*tan(s)
    [/tex]

    I am then suppose to write the maple code and send it to my instructor. The problem is that when I do the plot3d with those equations I get a strange looking thing that looks nothing like what a hyperbolic paraboloid should look like. I did the implicitplot3d for the equation to see what it should look like so I know I am way off.

    Can anyone offer me any hints?

    Thanks
     
  2. jcsd
  3. Sep 15, 2005 #2
    My equations might be right but I have the wrong domain for s and t. This is the code
    Code (Text):

    with(plots);

    plot3d([2*tan(t)*sec(s), sqrt(2)*sec(t)*sec(s), 3*tan(s)], t=-4*Pi..4*Pi, s=-4*Pi..4*Pi);
     
    And compare that with
    Code (Text):

    restart; with(plots);

    implicitplot3d(y^2/2-x^2/4-z^2/9=1, x=-10..10, y=-10..10, z=-10..10, grid=[20,20,20]);
     
     
  4. Sep 16, 2005 #3
    bump...

    Can anyone offer me any ideas?
     
  5. Sep 16, 2005 #4

    Tom Mattson

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    Staff Emeritus
    Science Advisor
    Gold Member

    Your equations are correct. And you're right about having a problem with your domains. The sec and tan functions both have multiple vertical asymptotes in the interval [itex][-4\pi,4\pi][/itex], so you'll have to do something about that.
     
  6. Sep 16, 2005 #5
    Thanks Mr. Mattson

    I finally got the graphs to look reasonable. You're right about the asymptotes being the problem of course. If I go from -Pi/4 to Pi/4 for both s and t, things look good. To get both sheets I used the following code

    Code (Text):
     
    with(plots);  
     
    surface1:=plot3d([2*tan(t)*sec(s), sqrt(2)*sec(t)*sec(s), 3*tan(s)], t=-P/4i..Pi/4, s=-Pi/4..Pi/4):  
    surface1:=plot3d([2*tan(t)*sec(s), -sqrt(2)*sec(t)*sec(s), 3*tan(s)], t=-P/4i..Pi/4, s=-Pi/4..Pi/4):  
    display(surface1, surface2);  
     
    But thanks again Tom...
    :smile:
     
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