There can be infinitely many lines: think of the longitudes through he North and South poles. However, there can be only one straight line.
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there are 6 lines can pass through 4 noncollinear points.
Only one line can be drawn through eight points.
An infinite number of lines can be drawn through a single point, but only one through two points (of course, if the points don't have the same coordinates).
Since the question does not require them to be straight lines, the answer is infinitely many.
If you're talking about straight lines (not curves) the answer is one.