It is known that any ellipsoid with principal semi-axes a, b, c has circular planar sections (https://en.wikipedia.org/wiki/Circular_section). 

- Is the largest circular disk contained within any ellipsoid given by one of its circular sections? If so, does this property hold for any quadric which has circular sections?

- What is the expression for the radius of the largest contained disk  in an ellipsoid in terms of a, b, c?