Chapter 12.6, Problem 13E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Use traces to sketch and identify the surface.

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

**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

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