   Chapter 11.6, Problem 18E

Chapter
Section
Textbook Problem

# Sketching a Quadric SurfaceIn Exercises 15–26, classify and sketch the quadric surface. Use a computer algebra system or a graphing utility to confirm your sketch. z 2 − x 2 − y 2 4 = 1

To determine

To graph: The given quadric surface z2x2y24=1 and then verify it by using a computer algebra system or a graphing utility.

Explanation

Given:

The given quadric surface is z2x2y24=1.

Graph:

z2x2y24=1

To find the sketch of surface, first make the traces of the surface with respect to three planes of the coordinate axis.

The first trace is of xy-plane (z=0) is,

z2x2y24=1

Substitute z=0 in the above equation.

x2y24=1

This does not represent any shape.

The second trace is of yz-plane (x=0) is,

z2x2y24=1

Substitute x=0 in the above equation.

z2y24=1

Compare it with standard form of hyperbola, so the second trace is hyperbolic in nature.

The third trace is of xz-plane (y=0) is,

z2x2y24=1

Substitute y=0 in the above equation

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