   Chapter 12.1, Problem 32E

Chapter
Section
Textbook Problem

# Describe in words the region of ℝ3 represented by the equation(s) or inequality.32. x2 + y2 = 4

To determine

To describe: The representation of equation x2+y2=4 in 3 .

Explanation

3 is the three dimensional coordinate system which contains x, y, and z-coordinates.

The equation x2+y2=4 has no restrictions on z-coordinate and it is a circle in any horizontal plane z=k . Therefore, the surface x2+y2=4 in 3 consists of all possible horizontal circles x2+y2=4 , z=k .

It is also described as follows.

Write the expression of circular cylinder along the z-axis.

x2+y2=r2 (1)

Here,

The equation x2+y2=4 is also written as x2+y2=22

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