## intersectionA place where two or more things meet or overlap. Two lines or curves intersect at a point, two planes can intersect in a line, and so forth. The intersection of two or more sets , represented by , is the set of elements that all the sets have in common; in other words, all the elements contained in every one of the sets. In plane geometry, an intersection is the crossing of two lines or curves at a point known as the point of intersection. In terms
of analytic geometry, if two
lines have equations y = f(x) and y = g(x)
where f(x) and g(x) are functions
of x, their points of intersection are given by those values of
x for which f(x) = g(x). For example, the line
y = 2x intersects the curve y = x^{2}
in two points whose coordinates are given by solution of the equation 2x
= x^{2}; this has two roots,
0 and 2, and hence the points of intersection are (0,0) and (2,4). Should
the equation f(x) = g(x) have roots that are not unique
(i.e., two or more are equal), then the curves are tangential at the point
or points defined by the equal roots. ## Related category• MATHEMATICAL TERMINOLOGY | |||||

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