Chapter 12.6, Problem 34E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Reduce the equation to one of the standard forms, classify the surface, and sketch it.

*y*^{2} = *x*^{2} + 4*z*^{2} + 4

To determine

**To classify**: The given surface equation and sketch the surface equation.

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

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

The value of *a* is

The value of *b* is

The value of *c* is

**Case i:**

Let

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

The trace of this expression in

**Case ii:**

Let

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