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.

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.

klimenkov · Answer

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.