Question

Find the equation of the ellipsoid passing through the points (±6,0,0),(0,±7,0) and (0,0,±5)

Answer 1

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

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