   Chapter 12.6, Problem 20E

Chapter
Section
Textbook Problem

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

To determine

To identify: The given surface equation and sketch it.

Explanation

Given data:

Surface equation is x=y2z2 .

Formula used:

Consider the standard equation of a hyperbolic paraboloid along the x-axis.

xa=y2b2z2c2 (1)

Consider the given surface equation.

x=y2z2 (2)

Modify the equation.

x1=y21z21 (3)

By comparing equation (3) with (1), the given surface equation satisfies the equation of a hyperbolic paraboloid along the x-axis.

Thus, the surface equation x=y2z2 is a hyperbolic paraboloid centered at origin.

Find a, b, and c by comparing equation (3) with equation (1).

a=1

The value of a is 1.

b2=1b=1b=±1

The value of b is ±1 .

c2=1c=1c=±1

The value of c is ±1 .

Case i:

Let x=k

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