Hutchinson–Zaharescu parabolas and Ford circles

In this note, we study properties of certain parabolas which were recently defined by Hutchinson and Zaharescu in their paper on parabolas infiltrating the Ford circles. We examine this connection between Ford circles and these parabolas. In particular, we characterize the intersection points of these parabolas in terms of tangent Ford circles. Further, we provide a finer analysis of area under the arcs of these parabolas with end points joining the centers of two neighboring Ford circles, than discussed in their paper.