Mathwords logoReference LibraryMathwords

Directrix of a Parabola

Directrix of a Parabola

A line perpendicular to the axis of symmetry used in the definition of a parabola. A parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix.

 

Parabola with focus point, directrix line below, and equal distances L1 (to focus) and L2 (to directrix) shown by arrows.

 

Example:  

Graph of upward-opening parabola with vertex at (3,-2), focus above vertex, vertical axis of symmetry at x=3, and horizontal...

This is a graph of the parabola Equation of a parabola: y = (1/4)x² − (3/2)x + 1/4 with all its major features labeled: axis of symmetry, focus, vertex, and directrix.

 

See also

Directrices of an ellipse, directrices of a hyperbola