Chapter 12.6, Problem 28E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Match the equation with its graph (labeled I-VIII). Give reasons for your choice.

*y* = *x*^{2} − *z*^{2}

To determine

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

Explanation

**Given data:**

Surface equation is

**Formula used:**

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

Consider the given surface equation.

Modify the equation.

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).

The value of *a* is

The value of *b* is 1.

The value of *c* is

**Case i:**

Let

Substitute *k* for *x* in equation (2),

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

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