Question

Find an equation of the ellipsoid which passes through (1,1,2) (0,0,3) (1,2,1) and has the coordinate planes as planes of symmetry.

Answer 1

The last condition gives you that the center of the ellipsoid will be in (0,0,0).
So the equation of this ellipsoid will be:\[\frac {x^2} {a^2} +\frac {y^2} {b^2}+\frac {z^2} {c^2}=1\]You have 3 points. Put them into this equation and get 3 equations and 3 unknowns - \(a,b,c\) and then solve it and get the answer.