   Chapter 12.6, Problem 17E

Chapter
Section
Textbook Problem

# Use traces to sketch and identify the surface. x 2 9  +  y 2 25  +  z 2 4  = 1

To determine

To identify: The given surface equation and sketch it.

Explanation

Given:

Surface equation is x29+y225+z24=1.

Formula used:

Consider the standard equation of an ellipsoid.

x2a2+y2b2+z2c2=1 (1)

Consider the given surface equation.

x29+y225+z24=1 (2)

By comparing equation (2) with (1), the given surface equation satisfies the equation of an ellipsoid, which is centered at the origin.

Thus, the surface equation x29+y225+z24=1 is an ellipsoid.

Find a, b, and c by comparing equation (2) with equation (1).

a2=9a=9a=±3

The value of a is ±3.

b2=25b=25b=±5

The value of b is ±5.

c2=4c=4c=±2

The value of c is ±2.

Let x=k.

Substitute k for x in equation (2),

k29+y225+z24=1

y225+z24=1k29 (3)

Modify equation (3) for k=3,

y225+z24=1329y225+z24=199y225+z24=11y225+z24=0

Simplify the equation

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