Chapter 12.6, Problem 23E

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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 one sheet along the *y* axis.

Consider the given surface equation.

Rearrange the equation.

By comparing equation (3) with (1), the computed expression satisfies the equation of hyperboloid of one sheet.

**Case i:**

Let

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

Modify equation (4) for

The integer solution of this equation is,

Hence, the surface equation has a origin point for

Substitute 0 for *y* and *z* in equation (4),

Similarly, the surface equation (4) have two different oriented hyperbolas trace for

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