Chapter 12, Problem 33RE

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Identify and sketch the graph of each surface.

**33.** −4*x*^{2} + *y*^{2} −4*z*^{2} = 4

To determine

**To identify**: The given surface equation and sketch it.

Explanation

**Given data:**

Surface equation is

**Formula used:**

Consider the standard equation of hyperboloid of two sheets.

Consider the given surface equation.

Rearrange the equation.

By comparing equation (3) with (1), the computed expression satisfies the equation of hyperboloid of two sheets.

Thus, the surface equation

**Case i:**

Let

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

The trace of this expression in

**Case ii:**

Let

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

The trace of this expression in

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