Chapter 12, Problem 34RE

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Identify and sketch the graph of each surface.

**34.** *y*^{2} + *z*^{2} = 1 + *x*^{2}

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 one sheet along the *x* axis.

Consider the given surface equation.

Rearrange the equation.

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

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 *y* in equation (2),

Modify equation (4) for

The integer solution of this equation is,

Hence, the surface equation has a origin point for

Substitute 0 for *x* and *z* in equation (4),

Similarly, the surface equation (4) have two different oriented hyperbolas trace for

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