Question

9. A and B are equidistant from the line l. How many circles can be drawn with their centres on line l and that pass through both A and B? Please explain the reasoning also!!

Answer 1

>10

Answer 2

Do not assume that a circle must have its origin where AB intersects the line l.
You could take any point on line l and use if as the center of a circle such that the distance from that point to either A or B is the radius.