Max/Min Value Problem

Suppose I have a standard 3-dimensional egg-shaped ellipsoid with the
following equation:

(x^2)/(a^2) + (y^2)/(b^2) + (z^2)/(c^2) = 1

If I rotate the ellipsoid around the y-axis, x-axis, then z-axis I am
left with an equation of the form:

Ax^2 + By^2 + Cz^2 + Dx + Ey + Fz + Gxy + Hxz + Iyz + J = 0

,where A,B,C,D,E,F,G,H,I,J are constants resulting from rotation
matrices.

How do I find the max/min values of x and y ?