Learn how to draw an elliptic and a hyperbolic paraboloid.

At this point, there are two basic surfaces that you should get to know quite well:
  • Elliptic paraboloids.
  • Hyperbolic paraboloids.

For both of these surfaces, if they are sliced by a plane perpendicular to the plane , the cross-section looks like a parabola, hence the name paraboloid.

Drawing an elliptic paraboloid

We’ll start with elliptic paraboloid that opens up, like . You begin by drawing a set of axis:

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Now draw a parabola in the -plane:
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Now add-in an ellipse:
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To draw an elliptic parabolid opening down, like you draw something like this:
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Drawing a hyperbolic paraboloid

The hyperbolic parabolid often gives people more trouble. Let’s teach you the tricks of the trade. Let’s first draw Note here, as the absolute value of increases, the -values increase. As the abosolute value of increase, the -values decrease. We’ll see this in our drawing. You begin by drawing a set of axis:

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Now draw a parabola in a -plane that contains some positive -value.
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Now draw a curvy line:
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And another parabola:
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Finally, add in the base:
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And you have a hyperbolic paraboloid!