Chapter 12.6, Problem 38E

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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} + *z*^{2} − 24*x* − 8*y* + 4*z* + 55 = 0

To determine

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

Explanation

**Given data:**

Surface equation is

**Formula used:**

Consider the standard equation of an ellipsoid.

Consider the given surface equation.

Rearrange the equation.

Find the center by using equation (3).

As the computed expression (3) satisfies the equation of ellipsoid, which is centered at

Thus, the surface equation

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

The value of *a* is
*x*-axis is

The value of *b* is
*y*-axis is

The value of *c* is
*y*-axis is

**Case i:**

Let

Substitute *k* for *x* in equation (3),

Modify equation (4) for

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