The set of all points in a plane such that the difference of the distances from two fixed points, called

*foci*, is constant.- The midpoint of the segment that joins the foci is the
*centre of the hyperbola*. - The line that passes through the two foci is the
*transverse axis*and the line that passes through the centre, and that is perpendicular to the transverse axis, is the*conjugate axis*. - The basic equation of the relation that defines a hyperbola in a Cartesian plane is \(\dfrac {x^{2}} {a^{2}}−\dfrac {y^{2}} {b^{2}} = 1\) where
*a*is the length of the semi-transverse axis and*b*is the length of the semi-conjugate axis. - The points with coordinates
*F*_{1}(*c*, 0) ou*F*_{2}(−*c*, 0), where*c*² =*a*² +*b*², are the foci of the hyperbola. - The hyperbola is
**equilateral**when*a*=*b*, that is, when the asymptotes are perpendicular.

- A hyperbola can also be described as a section of a right circular cone that is obtained when a plane cuts the two nappes of the cone but does not pass through its vertex.

### Etymological note

The term *hyperbola* is derived from two Greek words : υπερ *(huper)*, meaning “beyond,” and βαλλω (*ballô*), meaning “to throw”.