This paper presents a constructive and visually guided approach to characterizing conicoids—quadratic surfaces in three-dimensional space—as geometric loci. Extending the classical definition of a parabola as the set of points equidistant from a fixed point and a directrix, we propose analogous distance-based definitions for ellipsoids, hyperboloids, cones, and both elliptic and hyperbolic paraboloids. Additionally, we explore a higher-dimensional analogy by interpreting conicoids as spatial sections of a right 3-cone intersected with a 3-plane, in the same spirit that conic sections arise from planar cuts of a cone. The derivations are developed with pedagogical clarity and computational support, making use of the Wolfram Mathematica system to visualize and validate each geometric interpretation. This dual perspective—analytic and visual—provides an accessible framework for students and educators, enabling further exploration in symbolic computation and dynamic geometry. The methodology is particularly suitable for academic settings that integrate traditional geometry with modern computational tools, offering a bridge between classical theory and contemporary mathematical practice.