Answered: EXAMPLE 2 An ellipsoid The surface…

EXAMPLE 2 An ellipsoid The surface defined by the equation 1 is an ellipsoid. Graph the ellipsoid with a = 3, b = 4, and c = 5.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter7: Conic Sections

Section7.2: Ellipses

Problem 4E: Label the vertices and foci on the graphs given for the ellipses in Exercises 2 and 3....

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Question

EXAMPLE 2 An ellipsoid The surface defined by the equation
1 is
an ellipsoid. Graph the ellipsoid with a = 3, b = 4, and c = 5.

Expert Solution

Given,

$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1$

Put $a = 3, b = 4, and c = 5$ , we get

$\frac{x^{2}}{3^{2}} + \frac{y^{2}}{4^{2}} + \frac{z^{2}}{5^{2}} = 1 \Rightarrow \frac{x^{2}}{9} + \frac{y^{2}}{16} + \frac{z^{2}}{25} = 1$

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