infinite number of circles which can pass through two point

We can see points A and B. Five circles have been drawn which pass through the two points A and B. These five circles are a, b, c, d and e. We can freely move points A and B and observe how the sizes and positions of the circles change.
Questions to think about 1. Let us think how many circles can be drawn which pass through points A and B? 2. Let us think how we can draw an infinite number of circles which pass through two given points?