Chapter 12, Problem 31RE

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Identify and sketch the graph of each surface.

**31.** *x*^{2} = *y*^{2} + 4*z*^{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 elliptic cone along the *x* axis.

Consider the given surface equation.

By comparing equation (2) with (1), the computed expression satisfies the equation of an elliptic cone.

Therefore, the surface equation

**Case i:**

Let

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

Modify equation (3) for

The integer solution of this equation is,

Hence, the surface equation has a origin point for

Similarly, trace of the surface equation is empty for

**Case ii:**

Let

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

The trace of this expression represents a hyperbola for

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