The path of a point that moves in a plane such that the difference of the distances from the two fixed points (foci) to any point in the path stays constant, in which the constant must be less than the distance between the two fixed points. A hyperbola has two branches and two axes of symmetry. The axis through the foci (transverse axis) cuts the hyperbola at two vertices. The axis, which is at a right angle to the transverse axis through the center of the hyperbola, is called a conjugate axis.
In Cartesian coordinates, the equation of a hyperbola with its center at the origin and the transverse axis along the x-axis is as follows:
x2/a2 - y2/b2 = 1
in which 2a is the length of the transverse axis and 2b is the length of the conjugate axis.
The asymptotes have the equations:
x/a + y/b = 0
x/a - y/b = 0