   Chapter 11.6, Problem 13E

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. x 2 + y 2 4 + z 2 = 1

To determine

To graph: The given quadric surface x21+y24+z21=1 and then verify it by using a computer algebra system or a graphing utility.

Explanation

Given:

The given quadric surface is x21+y24+z21=1.

Graph:

x21+y24+z21=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,

x21+y24+z21=1

Substitute z=0 in the above equation.

x21+y24=1

Compare it with standard form of ellipse, so the first trace is elliptical in nature.

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

x21+y24+z21=1

Substitute x=0 in the above equation

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