# locus

## locus in genetics

In genetics, the locus is the position on a chromosome where a specific gene is located.

## locus in mathematics

In mathematics, a locus is the set of all points (usually forming a curve or surface)
that satisfy some condition. For example, the locus of points in the
plane equidistant from a given point is a circle. Plural is 'loci.'
The Latin word *locus* simply means place.' (The Greek equivalent
is *topos*, which crops up in 'topology.') Some specific examples of loci are as follws.

1. The locus of points at a distance *r* from a fixed point *O* is the circle with center *O* and radius *r*.

2. The locus of points equidistant from two fixed points *A* and *B* is the perpendicular bisector of the line segment *AB*.

3. The locus of points at distance *d* from a straight line *l* comprises the pair of lines parallel to *l* at a distance *d* from it on either side.

4. The locus of points equidistant from two intersecting straight lines *l* and *m* is the pair of bisectors of the angle formed by *l* and *m*.

5. The locus of the centers of circles which pass through two fixed points *A* and *B* is the perpendicular bisector of the segment *AB*.

6. The locus of the centers of circles which touch a given straight line *l* in a given point *A* is the line through *A* perpendicular to *l*.

7. The locus of points the sum of whose distances from two fixed points *F*_{1} and *F*_{2} is constant and equal to 2*a* is the ellipse with foci *F*_{1} and *F*_{2} and major axis of length 2*a*.

8. The locus of points the differences of whose distances from two fixed points *F*_{1} and *F*_{2} is constant is the hyperbola with foci *F*_{1} and *F*_{2}.

9. The locus of points whose distances from a fixed point *F* and a fixed straight line *l* are equal is the parabola with focus *F* and directrix *l*.