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

The standard equation of an ellipsoid is given by

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

Therefore, the equation of the ellipsoid is given by

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