Locus: Difference between revisions

Latest revision as of 01:58, 22 March 2011

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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).

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 {{stub}}
-'''Locus''' is essentially a synonym for [[set]].  It is used most frequently in [[geometry]].
+'''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 ==
-'''Circle:'''
-A [[circle]] is the '''locus''' of all points a certain distance from a given center.
+* 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 <math>l</math> and a point <math>P</math>, a [[parabola]] is the locus of all points <math>S</math> such that <math>SP=</math> the distance from <math>S</math> to <math>l</math>.
-'''Parabola:'''
+* If we have two points A and B, an [[ellipse]] is the locus of all points <math>S</math> such that <math>SA+SB</math> is equal to a given constant.
+* Given two points <math>A</math> and <math>B</math> and a constant <math>k</math>, the locus of all points <math>P</math> that satisfy <math>\frac{PA}{PB} = k</math> is a circle (sometimes called an [[Apollonius circle]]).
-If we have a line <math>l</math> and a point <math>P</math>, a [[parabola]] is the '''locus''' of all points <math>S</math> such that <math>SP=</math> the distance from <math>S</math> to <math>l</math>.
-'''Ellipse'''
-If we have two points A and B, a [[ellipse]] is the '''locus''' of all points <math>S</math> such that <math>SA+SB</math> remains constant.
 [[Category:Geometry]]

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Locus: Difference between revisions

Latest revision as of 01:58, 22 March 2011

Examples