Difference between revisions of "Locus"
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| − | '''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 == | == Examples == | ||
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| − | A [[circle]] | + | * 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>. | |
| − | + | * 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 | ||
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| − | If we have two points A and B, | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
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
and a point 
, a parabola is the locus of all points 
such that 
the distance from to . - If we have two points A and B, an ellipse is the locus of all points such that
is equal to a given constant. - Given two points
and 
and a constant 
, the locus of all points that satisfy 
is a circle (sometimes called an Apollonius circle).
and a point 
, a 
such that 
the distance from 
is equal to a given constant.
and 
and a constant 
, the locus of all points 
is a circle (sometimes called an 
