This is a question for complex analysis - related to non-Euclidean geometry

(a) Show that for any two points in the upper half-plane there exists exactly one Lobachevsky straight line that passes through those points. That is, show that Euclid's 1st postulate is satisfied.

(b) Show that for any point in the upper half-plane and any direction there is a unique Lobachevsky straight line passing through that point and with tangent in the given direction.