The hyperbola is the locus of points on the plane whose difference of distances to two fixed points, foci, are constant.
Elements of the Hyperbola
The foci are the fixed points of the hyperbola. They are denoted by F and F'.
Transverse Axis or real axis
The tranverse axis is the line segment between the foci.
Conjugate Axis or imaginary axis
The conjuagate axis is the perpendicular bisector of the line segment (transverse axis).
The center is the point of intersection of the axes and is also the center of symmetry of the hyperbola.
The points A and A' are the points of intersection of the hyperbola with the transverse axis.
The focal radii are the line segments that join a point on the hyperbola with the foci: PF and PF'.
The focal length is the line segment , which has a length of 2c.
The semi-major axis is the line segment that runs from the centre to a vertex of the hyperbola. Its length is a.
The semi-minor axis is a line segment which is perpendicular to the semi-major axis. Its length is b.
Axes of Symmetry
The axes of symmetry are the lines that coincide with the transversal and conjugate axis.
The asymptotes are the lines with the equations:
The Relationship between the Semiaxes: