Chapter 12.6, Problem 24E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Match the equation with its graph (labeled I-VIII). Give reasons for your choice.

−*x*^{2} + *y*^{2} − *z*^{2} = 1

To determine

**To match**: The given surface equation with their corresponding graph shown in Figure I-VIII.

Explanation

**Given data:**

Surface equation is

**Formula used:**

Consider the standard equation of hyperboloid of two sheets.

Consider the given surface equation.

By comparing equation (2) with (1), the computed expression satisfies the equation of hyperboloid of two sheets.

**Case i:**

Let

Substitute *k* for *x* in equation (2),

The trace of this expression in

**Case ii:**

Let

Substitute *k* for *z* in equation (2),

The trace of this expression in

**Case iii:**

Let

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P-38RECh-12 P-1PCh-12 P-2PCh-12 P-5P

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