The title of this question might seem not so clear, as straight lines are by definition curves of zero curvature; however, i refer to lines in Poincare unit disk model, in which straight lines are modeled as portions of circles orthogonal to the boundary of the unit disk (i.e circle that intersects the unit circle at right angles).
Therefore, my question is: given the coordinates of two points in the Poincare disk, what is the curvature of the orthogonal circle connecting them? I prefer more conceptually transparent ways to arrive at the formula for curvature.