Which of the following is the correct definition of a circle found within a plane in terms of a center (h, k) and radius r?

All points whose x‑coordinate equals h and whose y‑coordinate is within r units of k.

The set of ordered pairs (x,y) such that (x–h)² + (y–k)² < r², after translation by (h,k).

All points whose average distance from (h,k) over any interval is equal to r.

The set of all points in the plane that are exactly distance r from the point (h,k).