Page "Hyperbola" Paragraph 11

At large distances from the center, the hyperbola approaches two lines, its asymptotes, which intersect at the hyperbola's center.

A hyperbola approaches its asymptotes arbitrarily closely as the distance from its center increases, but it never intersects them ; however, a degenerate hyperbola consists only of its asymptotes.

Consistent with the symmetry of the hyperbola, if the transverse axis is aligned with the x-axis of a Cartesian coordinate system, the slopes of the asymptotes are equal in magnitude but opposite in sign, ±, where b = a × tan ( θ ) and where θ is the angle between the transverse axis and either asymptote.

The distance b ( not shown ) is the length of the perpendicular segment from either vertex to the asymptotes.