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Homesecant line

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# secant line

The secant line (or simply the secant) of a curve is a straight line intersecting the curve in at least two distinct points. [The name is initially a participial form of the Latin verb secare ‘to cut’.]

If one sets a secant e.g. to the “cubic parabola” $y=x^{3}$ through its points $(0,\,0)$ and $(1,\,1)$, there is also a third common point $(-1,\,-1)$.

Notice that a secant line can also be tangent to the curve at some point, given that tangency is only a local property. In the following picture, $l$ is a secant line for the curve $C$ (since it intersects the curve at points $A$ and $B$), yet it is also a tangent line at the point $A$.

Defines:

cubic parabola

Related:

curve

Synonym:

secant, secant of the curve, secant to the curve

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

51M99*no label found*

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