# Focus

In geometry, the term **center point** is closely related to the concept of the geometric center of gravity . Last but not least, it is used in the following contexts:

- In the case of a segment , a circle , a sphere or in general an n-dimensional sphere , the center point is the point that has the same (minimum) distance from all points of this sphere . This definition can generally be made in (complete) metric spaces .
- In the case of conic sections and the second-order surfaces described by quadrics (e.g. ellipsoids or cones ), the center points are the fixed elements of a reflection , which transforms the given figure into itself. All
*conic sections*with the exception of the parabolas have exactly one center; a*surface of the second order*can have no, exactly one or a whole straight line or plane of centers. If it has exactly one center, it is referred to as a*center*quadric.

## Description by coordinates

### route

Is the end point and the starting point of a route is known, it can be the coordinates of the center point on the relationships , or in addition at a distance in space with determined.

### Circle / sphere

If a circular equation of the form is given, the coordinates of the center point can be specified directly via . In a ball, the equation is added to the Z-axis: . The center is thus .

## See also

## literature

- Grotemeyer, KP:
*Analytical Geometry,*Berlin: Göschen / de Gruyter Collection (4th edition 1969)

## Web links

**Wiktionary: Center point**- explanations of meanings, word origins, synonyms, translations