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Homework Help: Graphing in 3-d

  1. Aug 23, 2012 #1
    I am having difficulty graphing equatioins in 3D for instance...

    what does the graph in 3-D look like x^2 + z^2 ≤ 9?

    Apparently its a cylinder extending along the y-axis. My initial guess was it was a 2-D circle with radius 3 on the xz plane. Anyways how should I have known it extended along the y-axis?
  2. jcsd
  3. Aug 23, 2012 #2


    Staff: Mentor

    The statement of the problem probably says something about graphing the set of points (x, y, z) such that x2 + z2 ≤ 9.

    Since the inequality doesn't include a y term, the y coordinates are completely arbitrary. That's why the graph extends along the y-axis.
  4. Aug 23, 2012 #3
    Another question... the 3d picture is on the paint doc and I am wondering why the entire surface is only in the first octant because isn't the point (which I hightligted in the paint document) in the 3rd octant???

    Attached Files:

    • 3d.jpg
      File size:
      27.9 KB
  5. Aug 23, 2012 #4


    Staff: Mentor

    That graph is screwy.

    The graph of the equation z = 2x2 + 2y2 - 4 is a paraboloid that opens up from its vertex at (0, 0, -4), and whose central axis lies along the z-axis. In your picture, the thing appears to be in the first octant.
  6. Aug 23, 2012 #5


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    Science Advisor
    Homework Helper
    Gold Member

    It isn't in the first octant. It is correct. The planes that look like the coordinate planes aren't ##x=0## and ##y=0##. Look how the axes are labeled.
  7. Aug 24, 2012 #6


    Staff: Mentor

    Good point. I saw how the axes are labeled, but I didn't notice that the planes you see aren't the regular coordinate planes.
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