Can anyone please help me with this problem? I am stuck! **Problem Statement**Find the equation of the ellipsoid passing through the points $ (±8, 0, 0), (0, ±9, 0), (0, 0, ±4) $.**Solution Approach**To determine the equation of the ellipsoid, we use the standard form:\[\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1\]Given points include:1. $ (±8, 0, 0) $ implies $ \frac{8^2}{a^2} = 1 $, hence $ a^2 = 8^2 = 64 $.2. $ (0, ±9, 0) $ implies $ \frac{9^2}{b^2} = 1 $, hence $ b^2 = 9^2 = 81 $.3. $ (0, 0, ±4) $ implies $ \frac{4^2}{c^2} = 1 $, hence $ c^2 = 4^2 = 16 $.Thus, the equation of the ellipsoid is:\[\frac{x^2}{64} + \frac{y^2}{81} + \frac{z^2}{16} = 1\] **Problem Statement:**Find the equation of the ellipsoid passing through the points $(\pm 8, 0, 0)$, $ (0, \pm 3, 0) $, and $(0, 0, \pm 4)$.

Answered: Find the equation of the ellipsoid…

Math

Advanced Math

Find the equation of the ellipsoid passing through the points (+8, 0, 0), (0₁ +3,0) and (0,0₁ +4)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Can anyone please help me with this problem? I am stuck!

**Problem Statement**

Find the equation of the ellipsoid passing through the points $ (±8, 0, 0), (0, ±9, 0), (0, 0, ±4) $.

**Solution Approach**

To determine the equation of the ellipsoid, we use the standard form:

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

Given points include:

1. $ (±8, 0, 0) $ implies $ \frac{8^2}{a^2} = 1 $, hence $ a^2 = 8^2 = 64 $.

2. $ (0, ±9, 0) $ implies $ \frac{9^2}{b^2} = 1 $, hence $ b^2 = 9^2 = 81 $.

3. $ (0, 0, ±4) $ implies $ \frac{4^2}{c^2} = 1 $, hence $ c^2 = 4^2 = 16 $.

Thus, the equation of the ellipsoid is:

\[
\frac{x^2}{64} + \frac{y^2}{81} + \frac{z^2}{16} = 1
\]

**Problem Statement:**

Find the equation of the ellipsoid passing through the points $(\pm 8, 0, 0)$, $ (0, \pm 3, 0) $, and $(0, 0, \pm 4)$.

Expert Solution

Step 1

We need to find the equation of ellipsoid passing through the points $(\pm 8, 0, 0), (0, \pm 3, 0), (0, 0, \pm 4) .$

We know that an ellipsoid has the general equation, $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1$ where $a, b$ and $c$ are the principal semiaxes.

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