   Chapter 11.6, Problem 27E

Chapter
Section
Textbook Problem

# EXPLORING CONCEPTSHyperboloid Explain how to determine whether a quadric surface is a hyperboloid of one sheet or a hyperboloid of two sheets.

To determine

The six quadric surfaces and the standard form of each.

Explanation

The six quadric surfaces and their standard forms are:

Ellipsoid: x2a2+y2b2+z2c2=1 and the trace of ellipsoid is ellipse in xy,xz and yz plane.

Now using maple software, the graph of ellipsoid is,

Hyperboloid of one Sheet: x2a2+y2b2z2c2=1 and the trace of Hyperboloid of one Sheet is ellipse in xy, hyperbola in xz and yz plane.

Now using maple software, the graph of Hyperboloid of one Sheet is,

Hyperboloid of two Sheet: z2c2y2b2x2a2=1 and the trace of Hyperboloid of two Sheet is ellipse in xy, hyperbola in xz and yz plane.

Now using maple software, the graph of Hyperboloid of two Sheet is,

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