# 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 ‘’.]

If one sets a secant e.g. to the “cubic parabola” $y={x}^{3}$ through its points $(0,\mathrm{\hspace{0.17em}0})$ and $(1,\mathrm{\hspace{0.17em}1})$, 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 $A$.

Title | secant line |
---|---|

Canonical name | SecantLine |

Date of creation | 2013-03-22 14:50:34 |

Last modified on | 2013-03-22 14:50:34 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 15 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 51M99 |

Synonym | secant |

Synonym | secant of the curve |

Synonym | secant to the curve |

Related topic | curve |

Defines | cubic parabola |