   Chapter 12.6, Problem 14E

Chapter
Section
Textbook Problem

# Use traces to sketch and identify the surface.z2 − 4x2 − y2 = 4

To determine

To identify: The given surface equation and sketch it.

Explanation

Given data:

Surface equation is z24x2y2=4 .

Formula used:

Consider the standard equation of hyperboloid of two sheets.

x2a2y2b2+z2c2=1 (1)

Consider the given surface equation.

z24x2y2=4

Rearrange the equation.

4x2y2+z2=4 (2)

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

Thus, the surface equation z24x2y2=4 is a hyperboloid of two sheets.

Case i:

Let x=k .

Substitute k for x in equation (2),

4k2y2+z2=4y2+z2=4+4k2z2y2=4+4k2

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

Case ii:

Let y=k .

Substitute k for y in equation (2),

4x2k2+z2=44x2+z2=4+k2z24x2=4+k2

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

Case iii:

Let z=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

#### Convert the expressions in Exercises 8596 radical form. 34(1x)5/2

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Find the x- and y-intercepts of the graph of y=x22x3.

Calculus: An Applied Approach (MindTap Course List)

#### let f(x) = x 1, g(x) = x+1, and h(x) = 2x3 1. Find the rule for each function. 12. gf

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Evaluate the integrals in Problems 1-32. Identify the formula used. 25.

Mathematical Applications for the Management, Life, and Social Sciences

#### Evaluate the integral. 14. 01dx(x2+1)2

Single Variable Calculus: Early Transcendentals

#### What are the five steps of the scientific method?

Research Methods for the Behavioral Sciences (MindTap Course List) 