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Homework Help: Quadratic surfaces

  1. Jan 4, 2014 #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


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    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


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    what about the asymptotes?

    what does the 3D graph of the asymptotes look like? :wink:
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