Okay, if that is all what is given, then the center can be (2,0).
"Can be" only, because as your classmates said, the major axis should have been given. As it is, the center can be anywhere from (2,2) down to (2,-infinity), if the locations are in integers.
So why (2,0)?
Because if the center were really at (2,0) and the minor axis is 6 units long, then the "dimensions" of the ellipses are multiples of 3.
Focal length (focus to near vertex) = 3 units.
Major axis = 12 units
Minor axis = 6 units
Lame reason, I know.