   Chapter 3.P, Problem 14P

Chapter
Section
Textbook Problem

# Sketch the region in the place consisting of all points ( x , y ) such that 2 x y ≤ | x − y | ≤ x 2 + y 2

To determine

To sketch:

The region in the plane consisting of all points (x,y) such that 2xyx-yx2+y2

Explanation

1) Concept:

Make the two cases depend on x  y and y x. Then simplify the inequality by considering left inequality and right inequality, and then conclude about the required region.

2) Given:

2xyx-yx2+y2

3) Calculation:

Here to find the points x,y, consider two cases.

Case I) xy

If xy, this gives the points on or below the line y=x and the given inequality become

2xyx-yx2+y2

Solving the right inequality,

x-yx2+y2

0x2-x+y2+y

(x2-x)+(y2+y)0

x-122+y+12212

This is a circle with radius 12   and center 12,-12. Therefore, the points lie on or outside the circle.

Solving the left inequality,

2xyx-y

2xy-x+y0

xy-12x+12y0

x+12y-12-14

This is a hyperbola passing through the origin, and it approaches the lines x=-12 and y=12 like asymptotes, and therefore, the points lie on or below the right side of the hyperbola

### 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

#### In Exercises 107-120, factor each expression completely. 118. 8a2 2ab 6b2

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

#### Compute P9,9.

Understanding Basic Statistics

#### True or False: f(x) = 4x2 8x + 1 is increasing on (0, 1).

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### Describe the strengths and weaknesses of physiological measures.

Research Methods for the Behavioral Sciences (MindTap Course List) 