There is a unique circle with a given center and point

We can clearly see a circle with center ‘A’ and a point ‘B’ on its circumference. We can freely move these points ‘A’ and ‘B’ and observe how the size and position of the circle gets changed.
Questions to think about 1. How many circles do we get if we assign unique positions to ‘A’ and ‘B’? 2. Is it possible to get more than one circle with fixed positions of ‘A’ and ‘B’?