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!

Quadratic surfaces

  1. Jan 4, 2014 #1
    4x^2-y^2+2z^2+4=0
    x^2-y^2/4+z^2/2+1=0
    -x^2+y^2/4-z^2/2=1

    In the xy trace -x^2+y^2/4=1+k^2/2 taking k=0 will yield the hyperbola but what affect will z have on the resulting surface as it tends to +- infinity
    It appears to me that as z to +- infinity the hyperbola in the xy plane becomes wider and this is not the case in the graph
     
    Last edited: Jan 4, 2014
  2. jcsd
  3. Jan 4, 2014 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi nameVoid! :smile:

    (try using the X2 button just above the Reply box:wink:)
    k = 0 gives you the "horizontal" slice at z = 0

    k = k gives you the general "horizontal" slice at z = k

    so (for constant k) what is the shape of -x2+y2/4=1+k2/2 ? :wink:
     
  4. Jan 4, 2014 #3
    I'm plotting a few points and the change in y as x changes from 0 to 1 is less as z increases causing the hyperbola to be wider although in the resulting shape it appears to be narrowing

    The slice at z=0 should be the widest slice however at this point it has the greatist change in y as xbfrom 0 to 1

    Mathematica shows graphs as z becomes large to be within the former this is not the obvious case given the change pattern in y from x 0 to 1 but as z becomes large it looks to be less

    As becomes large the hyperbola must widen, although it is not as wide as the 0 cut it still must widen at slightly fast rate because if it's position with respect to x
     
    Last edited: Jan 4, 2014
  5. Jan 4, 2014 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    what about the asymptotes?

    what does the 3D graph of the asymptotes look like? :wink:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Quadratic surfaces
  1. Quadratic surface (Replies: 2)

  2. Quadratic surface (Replies: 2)

  3. Quadratic surface (Replies: 4)

  4. Quadratic surfaces (Replies: 1)

Loading...