# Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

Compute properties of the normal line to a curve at a given point

Contributed by:
Wolfram|Alpha Math Team

ResourceFunction["NormalLine"][ returns an association of properties of the normal line to | |

ResourceFunction["NormalLine"][ returns the value of the normal line property | |

ResourceFunction["NormalLine"][ returns information relating to one, among possibly several, of the normal lines to | |

ResourceFunction["NormalLine"][ returns information relating to one, among possibly several, of the normal lines to |

Allowed values of *prop* are:

"SlopeInterceptEquation" | equation of the normal line in slope intercept form |

"StandardFormEquation" | equation of the normal line in standard form |

"PointSlopeEquation" | equation of the normal line in point slope form |

"Slope" | slope of the normal line |

"PointOfNormalcy" | point at which the normal line is computed |

"HorizontalIntercept" | horizontal intercept for the normal line equation |

"VerticalIntercept" | vertical intercept for the normal line equation |

"Plot" | plot of the normal line equation |

All | association of information returning all allowed properties |

If *expr* does not have head Equal, then *expr* is treated as an expression defining *y* in terms of *x*. In other words, ResourceFunction["NormalLine"][*expr*,{*x*,*a*},*y*,…] is equivalent to ResourceFunction["NormalLine"][*y*==*expr*,{*x*,*a*},*y*,…] if *expr* has a head other than Equal.

If only one coordinate of the intersection point is given, the other coordinate is inferred. For expressions that are multivalued at the given value of *x* or *y*, information on only one of potentially several normal lines is returned.

Compute the slope-intercept equation of the normal line to a curve at a given point:

In[1]:= |

Out[1]= |

Visualize this result:

In[2]:= |

Out[2]= |

Compute the slope of this normal line:

In[3]:= |

Out[3]= |

Compute the horizontal intercept of this normal line:

In[4]:= |

Out[4]= |

Get the standard-form equation of this normal line:

In[5]:= |

Out[5]= |

Get an Association of properties of a normal line to a curve:

In[6]:= |

Out[6]= |

Get just the point-slope equation of this normal line:

In[7]:= |

Out[7]= |

The first argument to NormalLine can be an implicit definition of a curve:

In[8]:= |

Out[8]= |

If a normal line is parallel to a coordinate axis, its intercept with that axis is None:

In[9]:= |

Out[9]= |

Requesting normal line information about a point that is not on the curve will result in an error message:

In[10]:= |

Out[10]= |

If one coordinate is not specified, information on only one of the possible normal lines at the given coordinate value is returned:

In[11]:= |

Out[11]= |

Vertical normal lines have infinite slope. Some of their properties may not be defined:

In[12]:= |

Out[12]= |

If a function has a cusp or a discontinuity at the given point, no normal line is returned:

In[13]:= |

Out[13]= |

- 3.1.0 – 04 August 2023
- 3.0.0 – 23 March 2023
- 2.0.1 – 29 March 2022
- 2.0.0 – 26 May 2021
- 1.0.0 – 08 March 2021

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