Chapter 12.6, Problem 32E

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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.

4*x*^{2} − *y*^{2} + 2*z*^{2} = 0

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 elliptic paraboloid along the *y* axis.

Consider the given surface equation.

Rearrange the equation.

By comparing equation (3) with (1), the computed expression satisfies the equation of elliptic paraboloid along the *y*-axis.

Thus, the surface equation
*y*-axis.

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 for

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