Hyperbolas from a distance-difference definition

Learn hyperbolas through their constant absolute difference of focal distances. Identify centers, transverse and conjugate axes, vertices and foci; reconstruct equations in either orientation and complete the square in general equations. These precalculus exercises combine single-select and multiselect reasoning with worked explanations of signs, parameter conventions and real-locus conditions. Difficulty progresses from structural recognition to reconstruction and model feasibility.