Describe the geodesics (that is, hyperbolic straight lines) in either the disc model or the half-plane model of the hyperbolic plane. Explain what is meant by the statements that two hyperbolic lines are parallel, and that they are ultraparallel.

Show that two hyperbolic lines $l$ and $l^{\prime}$ have a unique common perpendicular if and only if they are ultraparallel.

[You may assume standard results about the group of isometries of whichever model of the hyperbolic plane you use.]