Analysis: cross C into a section (circle) parallel to the cone bottom, cross AS and BS at R and T, and cross the ellipse C at P and Q, which are the vertices of the short semi-axis of the ellipse (this is the key, can you make it clear? )。 In the circle, RT is the diameter and the length is 3 (can you count it? ), TC=2, RC= 1, so PC= root number 2 (note that PQ is perpendicular to RT, can you work it out? I don't know how to discuss it again.

The combination of solid geometry and analytic geometry is unusual and a bit difficult.