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Two points determine a unique line. Therefore, there are infinitely many circles that can pass through two given points. This is because a circle can be defined by its center, which can lie anywhere along the perpendicular bisector of the line segment connecting the two points.
A line segment has exactly two endpoints. If it had less, then it would just be a point. If it was more, then it wouldn't be a segment anymore.
Normally just the the one which is in the middle of the line segment
There are infinitely many lines perpendicular to this line. All of them have the slope of -4/3, if that fact is of any help to you.