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ee2oo 2 years ago 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.

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1. klimenkov

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.

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