Locus

Revision as of 02:58, 22 March 2011 by Math explorer (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

This article is a stub. Help us out by expanding it.

Locus is essentially a synonym for set. It is used most frequently in geometry, to denote a set of points satisfying a certain geometric condition.

Examples

  • A circle can be defined as the locus of all points that are a certain distance from a given center.
  • If we have a line $l$ and a point $P$, a parabola is the locus of all points $S$ such that $SP=$ the distance from $S$ to $l$.
  • If we have two points A and B, an ellipse is the locus of all points $S$ such that $SA+SB$ is equal to a given constant.
  • Given two points $A$ and $B$ and a constant $k$, the locus of all points $P$ that satisfy $\frac{PA}{PB} = k$ is a circle (sometimes called an Apollonius circle).