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I am trying to find the normal to an ellipsoid of the form

[tex] x^2/a^2 + y^2/b^2 + z^2 = 1 [/tex]

What I did is the following: Let

[tex] psi = x^2/a^2 + y^2/b^2 + z^2 [/tex]

then grad psi (and thus the normal) is:

[tex] grad (psi) = (2x/a^2, 2y/b^2, 2z) = n [/tex]

Could anyone tell me whether that is the correct approach to find the normal to an ellipsoid? Thanks a lot!