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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.

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Q: If a straight line intersects with a curve how many points do they have in common?
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