normal line

A normal lineMathworldPlanetmath (or simply normal or perpendicularPlanetmathPlanetmath) of a curve at one of its points P is the line passing through this point and perpendicular to the tangent lineMathworldPlanetmath of the curve at P.  The point P is the foot of the normal.

If the plane curvey=f(x)  has a skew tangentPlanetmathPlanetmath at the point  (x0,f(x0)),  then the slope of the tangent at that point is  f(x0)  and the slope of the normal at that point is  -1f(x0).  The equation of the normal is thus


In the case that the tangent is horizontal, the equation of the vertical normal is


and in the case that the tangent is vertical, the equation of the normal is


The normal of a curve at its point P always goes through the center of curvatureMathworldPlanetmath belonging to the point P.

In the picture below, the black curve is a parabolaPlanetmathPlanetmath, the red line is the tangent at the point P, and the blue line is the normal at the point P.

Title normal line
Canonical name NormalLine
Date of creation 2013-03-22 17:09:53
Last modified on 2013-03-22 17:09:53
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 17
Author pahio (2872)
Entry type Definition
Classification msc 26B05
Classification msc 26A24
Classification msc 53A04
Synonym normal of curve
Synonym normal
Synonym perpendicular
Related topic ConditionOfOrthogonality
Related topic ParallelCurve
Related topic SurfaceNormal
Related topic Grafix
Related topic NormalOfPlane
Defines foot of normal
Defines foot of perpendicular