   Chapter 12.6, Problem 24E

Chapter
Section
Textbook Problem

# Match the equation with its graph (labeled I-VIII). Give reasons for your choice.−x2 + y2 − z2 = 1

To determine

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

Explanation

Given data:

Surface equation is x2+y2z2=1 .

Formula used:

Consider the standard equation of hyperboloid of two sheets.

x2a2+y2b2z2c2=1 (1)

Consider the given surface equation.

x2+y2z2=1 (2)

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

Case i:

Let x=k .

Substitute k for x in equation (2),

k2+y2z2=1y2z2=1+k2

The trace of this expression in x=k represents hyperbolas.

Case ii:

Let z=k .

Substitute k for z in equation (2),

x2+y2k2=1x2+y2=1+k2y2x2=1+k2

The trace of this expression in z=k represents hyperbolas.

Case iii:

Let y=k

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 