Find the equation of the ellipsoid passing through the points

Asked by maham237 @ 01/06/2021 in Mathematics viewed by 336 People

(±6,0,0),(0,±7,0) and (0,0,±5)

Answered by maham237 @ 01/06/2021

The standard equation of an ellipsoid is given by

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

where a, b and c are semi axes length. It means the ellipsoid is passing through the points (±a,0,0),(0,±b,0) and (0,0,±c).

Now, we have been given that the ellipsoid is passing through the points (±6,0,0),(0,±7,0) and (0,0,±5). Thus, we have

$a=\pm 6\\
b=\pm 7\\
c=\pm 5\\$

Therefore, the equation of the ellipsoid is given by

$\frac{x^2}{(\pm 6)^2}+\frac{y^2}{(\pm 7)^2}+\frac{z^2}{(\pm 5)^2}=1\\
\\
\frac{x^2}{36} +\frac{y^2}{49} +\frac{z^2}{25} =1$

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