A circle can be drawn with any center and any radius

We can see a circle in black color with center A. Point B is present on the circumference of this circle. We can move the points A and B. Change the positions of A and B of and observe how the position and size of the circle changes. Equation of the circle ‘c’ is mentioned in black color. Coordinates of point A and radius are mentioned in the circle
Questions to think about 1. Change the positions of A and B to get a number of unique circles. Does each unique circle have a unique center and a fixed radius or can we get multiple centers or radii for any of the unique circles