contour plots can be used in mathematica to plot equations such as ellipsoids like:
1/10^2*x^2 + 1/6^2*y^2 + 1/15^2*z^2 == 1
a command like:
ContourPlot3D[
1/10^2*x^2 + 1/6^2*y^2 + 1/15^2*z^2 == 1, {x, -11, 11}, {y, -7,
7}, {z, -16, 16}]
creates the ellipsoid