A # 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 F1 and F2 is constant and equal to 2a is the ellipse with foci F1 and F2 and major axis of length 2a.

8. The locus of points the differences of whose distances from two fixed points F1 and F2 is constant is the hyperbola with foci F1 and F2.

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.