In Poincare half-plane model,
$M = \{(x,y) \in \mathbb R^2 \mid y > 0\}$ and $ds = \frac{1}{y^2}(dx^2 + dy^2)$.
In wiki (https://en.wikipedia.org/wiki/Poincar%C3%A9_half-plane_model), it says that geodesic (straight line) "looks" like semicircles. Can anyone please show me an explicit derivation how to find a geodesic? I have been looking for examples, but could find none.