   Chapter 12.6, Problem 22E

Chapter
Section
Textbook Problem

# Match the equation with its graph (labeled I-VIII). Give reasons for your choice.9x2 + 4y2 + z2 = 1

To determine

To match: The given surface equation with their corresponding graph shown in Figure I-VIII.

Explanation

Given data:

Surface equation is 9x2+4y2+z2=1 .

Formula used:

Consider the standard equation of ellipsoid.

x2a2+y2b2+z2c2=1 (1)

Consider the given surface equation.

9x2+4y2+z2=1

Rearrange the equation.

x219+y214+z21=1 (2)

By comparing equation (2) with (1), the computed expression satisfies the equation of ellipsoid.

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

a2=19a=19a=±13

So, ellipsoid points on the x axis is (13,0,0) and (13,0,0)

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