# intersection

An intersection is a 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* = 2*x* intersects the curve *y* = *x*^{ 2} in two points whose coordinates are given by solution of the equation 2*x* = *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.