Horocyclic is an adjective used to describe a curve that intersects a family of circles. It has specific meaning in mathematics, but if you're looking for synonyms to describe this type of curve, consider using words like circular or cyclical. Other words that could work include curvilinear, rounded, or orbital. If you're looking for technical terminology, you could use the word epicyclic, which refers specifically to curves that move within other curves. The word helical might also apply, though it implies a more three-dimensional, twisting curve than a simple horocyclic one. Whatever word you choose, just make sure it accurately describes the nature of the curve you're talking about.