If F signifies "focus", and V is for "vertex", then the vertical line x=2 is where the major axis is. Because a vertex is an endpoint of the major axis and a focus is in the major axis. The major axis can be described as vertex-focus-center-focus-vertex.

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.