   Chapter 12.6, Problem 28E

Chapter
Section
Textbook Problem

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

To determine

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

Explanation

Given data:

Surface equation is y=x2z2 .

Formula used:

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

yb=x2a2z2c2 (1)

Consider the given surface equation.

y=x2z2 (2)

Modify the equation.

y1=x21z21 (3)

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

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

a2=1a=1a=±1

The value of a is ±1 .

b=1

The value of b is 1.

c2=1c=1c=±1

The value of c is ±1 .

Case i:

Let x=k .

Substitute k for x in equation (2),

y=k2z2

This expression represents the parabola along the negative y-direction for any values of k. So, the surface equation having a traces of parabola for x=k

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