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common point
is the result after doing intersection on 2 or more sets. It contains the elements which are common to all the sets on which intersection were done.
The intersection of two or more mathematical objects is the set of all points that are common to all of them. In set theory, that would be the elements in common. In geometry, it would be the set of all points in common. For example, the intersection of two different planes is a line; the intersection of a plane and a cone are the conic sections: circle, ellipse, parabola and hyperbola.
The intersection or point of intersection