Mathematics

Problem

Given fixed points

A(2, 0)

and

B(4, 0)

, and a moving point

C

on the circle

x^{2} + y^{2} = 36

. Determine if the locus of the centroid of

\triangle ABC

intersects the

y

-axis. If yes, find the length of the intercept cut off on the

y

-axis.