Plane z = 1 The trace in the z = 1 plane is the ellipse x2 y2 8 = 1, shown below 6Their defining characteristic is that their intersections with planes perpendicular to any two of the coordinate axes are hyperbolas There are two types of hyperboloids the first type is illustrated by the graph of x 2 y 2 z 2 = 1, which is shown in the figure below As the figure at the right illustrates, this shape is very similar to the one commonly used for nuclear power plant cooling2 The graph of (x 3)2 (y2)2 (z 1)2 = 16 is a of radius centered at 3 The shortest distance from the point (4, 0, 5) to the sphere (x 1)2 (y 2)2 z = 36 is 4 Let S be the graph of x² 2?
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