there are 6 lines can pass through 4 noncollinear points.
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A circle has infinitely many points of symmetry. Every straight line that passes through the center of a circle is a line of symmetry.
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.