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Sketching surfaces

  1. Jan 24, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm also having trouble with these:

    provide the names and sketch the following surfaces:
    x2+y2+z2=16
    x2+y2=9
    x2+2y2+4z2=16
    z=-√(9-x2-y2)
    z=√x2+y2
    z=x2+y2

    2. Relevant equations



    3. The attempt at a solution

    So for the first one it's a sphere with radius of 4, yes? And the second is a circle with radius three. These seem fairly obvious but I'm not sure how to go about visualizing the rest...is this something I just need to pick up on or is there a method I should be using?
     
  2. jcsd
  3. Jan 24, 2012 #2

    lanedance

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    once again taking cuts is good

    for 3) this looks like a sphere squashed along certain axes

    take z=0, this give
    x^2+2y2=16
    at y=0, x=4
    at x=0, y=2sqrt(2)

    which is an oval, once again try sketching it
     
  4. Jan 24, 2012 #3

    LCKurtz

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    A circle isn't a surface. The trace of this surface in the xy plane is a circle. In fact in the plane z = any constant its trace is a circle. So the surface itself is a circular cylinder. This is typical of equations that have a missing variable. The trace projects itself in the direction of the missing variable.
    Often all you need to do is draw the traces in the coordinate planes and sometimes one or two other planes to get an idea what the surface looks like. For example, for your last one the traces in the z-x and z-y planes are parabolas and the trace in the z = 4 plane is a circle. So...
     
  5. Jan 24, 2012 #4

    lanedance

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    good points
     
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