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Homework Help: Finding traces

  1. Oct 8, 2013 #1
    This is just a coursework question ( I didn't know where to post this). When I find the traces of an equation ( let's say x^2+y^2-z^2=1 for the sake of argument). How does it affect my graph if one part of the equation is an ellipse and the other is an hyperbola? I mean in this case I would expect to be like this

    When z=0

    x^2+y^2=1 --> ellipse (well a circle but a circle is an ellipse)

    when x=0

    y^2-z^2=1 --> hyperbola

    when y = 0

    x^2-z^2=1 --> hyperbola

    How does this affect the graph in 3d? I mean if it is both an ellipse and hyperbola, I can't visualize it geometrically.

    Sorry if this is the wrong section
  2. jcsd
  3. Oct 8, 2013 #2


    Staff: Mentor

    This is the right section, but you need to include the problem template, not just discard it. It's there for a reason.

    The traces are just the cross sections of the surface in the x-y, x-z, and y-z coordinate planes. You are not limited to just those cross sections. It might be useful to calculate the cross-sections in some other planes, such as z = 1 and z = -1. [STRIKE]You might also note that the surface doesn't extend above the plane z = 1 or below the plane z = -1.[/STRIKE]
    Edit: Deleted a sentence that resulted from misreading the problem.
    Last edited: Oct 8, 2013
  4. Oct 8, 2013 #3
    It wasn't an actual problem, I was reading in my book, there wasn't a problem per se. However, how do you notice it doesn't go above 1 and -1? I mean is it for this equation?
  5. Oct 8, 2013 #4


    Staff: Mentor

    I steered you wrong on that, by misreading a sign. Write the equation of the surface as x2 + y2 = z2 + 1, and look at what happens for cross sections that are perpendicular to the z-axis (i.e., horizontal cross sections).

    Each horizontal section is a circle whose radius increases as z increases. Due to symmetry, the cross sections below the x-y plane look the same as those above it. The minimum circle comes when z = 0.

    Do the hyperbola traces in the x-z and y-z planes start to make sense now?
  6. Oct 8, 2013 #5
    Yeah in the y-z I can see it how they'll never touch ( correct me if I'm wrong) same goes for x-z ( again correct me if I'm wrong)
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