   Chapter 7.2, Problem 47E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Classifying a Quadric Surface In Exercises 35-48, classify the quadric surface. See 25 x 2 + 25 y 2 − z 2 = 5

To determine

The quadric surface of equation 25x2+25y2z2=5.

Explanation

Given Information:

The equation of the quadric surface

25x2+25y2z2=5

Consider the given equation

5=25x2+25y2z2

Divide both sides of above equation by 5:

55=25x25+25y25z251=5x2+5y2z25

Now, reduce in standard form

1=x2(15)2+y2(15)2z25

Above equation is similar to the standard form of hyperboloid of one-sheet.

Standard form of hyperboloid

x2a2+y2b2z2c=1

Comparing above equation with 1=x2(15)2+y2(15)2z25:

a=15,b=15,c=5

Examine the equation 25x2+25y2z2=5 in vertical and horizontal planes

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