1. Limited time only! Sign up for a free 30min personal 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!

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

    Mark44

    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

    Mark44

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

Have something to add?
Draft saved Draft deleted