# Difference between revisions of "Locus"

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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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