Condition for axially symmetric ellipsoid

Question

Can someone help me understand what the condition is for an ellipsoid to be considered axially symmetric?

If I have an ellipsoid with a = 8.00e-07, then what should the values of the parameters b and c be such that I have an axially symmetric ellipsoid?

Answer 1

If we take the usual convention

$$a \ge b \ge c,$$

you can have an axially symmetric ellipsoid in one of the following two forms:

• either $a \ = b \ge c $ (oblate form),

• or $a \ge b \ = \ c$, (prolate form).

See here.

With of course the particular case $a = b = c$ for the sphere.