   Chapter 11.6, Problem 22E

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. 3 z = − y 2 + x 2

To determine

To graph: The given quadric surface 3z=y2+x2 and then verify it by using a computer algebra system or a graphing utility.

Explanation

Given:

The given quadric surface is 3z=y2+x2.

Graph:

3z=y2+x2

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,

3z=y2+x2

Substitute z=0 in the above equation.

0=y2+x2y2=x2y=±x

This equation represents straight line.

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

3z=y2+x2

Substitute x=0 in the above equation.

3z=y2z=(13)y2

Compare it with standard form of parabola, so the second trace is parabolic in nature.

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

3z=y2+x2

Substitute y=0 in the above equation

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