more generally, for every pencil of circles there exists a unique pencil consisting of the circles that are perpendicular to the first pencil. if one pencil is elliptic, its perpendicular pencil is hyperbolic, and vice versa; in this case the two pencils form a set of apollonian circles. the pencil of circles perpendicular to a parabolic pencil is also parabolic; it consists of the circles that have the same common tangent point but with a perpendicular tangent line at that point.