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Quadratic surface

  1. Dec 10, 2013 #1
    In equation z=y^2-x^2 when graphing the trace for y^2-x^2=k I see we have y=+-x for k=0 else y=+-sqrt(k+x^2) is there a simple way to graph this
     
  2. jcsd
  3. Dec 11, 2013 #2
    We'll to answer my own question I find it convenient to first take k=0 then we have y=+-x then taking k=1 and y=0 we have points (+-1,0) for k<0 then taking x=0 we have point (0,+-1) for k>0 now here we see that as y to +- infinity y will tend to the line y=+-x using lhopatols rule any thoughts here
     
  4. Dec 11, 2013 #3

    Mark44

    Staff: Mentor

    In addition to the horizontal cross sections you are plotting, it would be useful to plot the traces in the three coordinate planes. For example, in the y-z plane (when x = 0) you get z = y2, a parabola. In the x-z plane, you also get a parabola.
     
  5. Dec 11, 2013 #4
    Yes I am just interested in that particular trace is there's better way to graph it
     
  6. Dec 11, 2013 #5

    Mark44

    Staff: Mentor

    For y = ##\sqrt{x^2 + k}##, just plot some points. The graph of y = ##-\sqrt{x^2 + k}## is the reflection across the x-axis of the first one.
     
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