I have been told not to assume pieces of information that aren't told
That is correct.
I follow the explanation, but just curious if part of the question is missing OR it should just simply be understood given this question that the points form a circle?
The statement "A is 2 units away from (3, 4)" implies that A is a point on the circle, which center is (3, 4) and its radius is 2 units. So we are not given this fact directly, but deduce it from the statement.
Why is it so? Take any point on the circle. It will be exactly 2 units away from (3, 4). Take any point, which is not on the circle, and its distance to (3, 4) will be more or less than 2 units.
Any time you are given "A is r
units away from B" on a plane, then you know that A lies somewhere on the circle, which radius is r
units and the center is B. If point A is fixed and point B is unknown, then this phrase means that B lies somewhere on the circle, which radius is r
and the center is A.