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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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

z 2 = 2 x 2 + 2 y 2

To determine

The quadric surface of equation z2=2x2+2y2.

Explanation

Given Information:

The equation of the quadric surface

z2=2x2+2y2

Standard form of elliptical cone

x2a2+y2b2z2c=1

Special case, for circular cone

a=b

Consider the given equation

z2=2x2+2y2

Now, reduce in standard form

x2+y2z22=0

Above equation can be written as:

x212+y212z2(2)2=0

Above equation is similar to the standard equation of elliptic cone

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