Question 396635
With only 2 points, you can put a unique straight line thru them.
If it's any type of curve you have to specify what type curve.
eg, if it's a circle and one point is the center, then that's sufficient.
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But if it's 2 points on the circle, then an infinite # of circles can be made to pass thru them.
The same for parabolas, hyperbolas, and all conic sections.
If you have 3 points and the type of conic section, that's sufficient.
If you have 5 points and know that it's a conic section, that's sufficient.
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A general polynomial can be found to pass thru any number of points.