one and only one point no matter how far produced.
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tangent
It depends what kind of curve you're talking about. if it's a circle, and the line is tangent to the circle, then one. If it's a circle, and the line is not tangent to the circle, then two. But if it's a goofy shaped curve then it could be any number. But the most likely answer to your question is 2.
A secant line touches a circle at two points. On the other hand a tangent line meets a circle at one point.
A tangent of a circle is a straight line that touches the circle at only one point.
A line can be tangent to a circle in which case it intersects it in one point, it can intersect it in two points, or no points at all. So the choices are 0,1 or 2.