Difference between revisions of "Locus"

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'''Locus''' is essentially a synonym for [[set]].  It is used most frequently in [[geometry]].
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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 ==
 
== Examples ==
'''Circle:'''
 
  
A [[circle]] is the '''locus''' of all points a certain distance from a given center.
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* A [[circle]] can be defined as the locus of all points that are a certain distance from a given center.
 
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* 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:'''
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* 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.
 
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* 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]]
 
[[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 $l$ 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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