   Chapter 11.6, Problem 16E

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. − 8 x 2 + 18 y 2 + 18 z 2 = 2

To determine

To graph: The surface which is represented by the equation 8x2+18y2+18z2=2.

Explanation

Given:

The surface is represented by the equation

8x2+18y2+18z2=2

Graph:

Now, the provided equation is

8x2+18y2+18z2=2

Divide both sides by 2

4x2+9y2+9z2=1

Rewrite the equation as

y21/9+z21/9x21/4=1

The standard equation of hyperboloid of one sheet centered on z- axis is x2a2+y2b2z2c2=1

Since, the axis of hyperboloid corresponds to the variable whose coefficient is negative.

So, the standard equation of hyperboloid of one sheet centered on x- axis is y2b2+z2c2x2a2=1

The above equation matches with the gi

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