This study investigates the locus of a point P in the plane determined by three distinct points A,B,O, under the condition ∠OPB≡∠APO. Using complex coordinates, we derive the equation of the curve and employ it to rigorously prove the observed properties, while also providing geometric interpretations for some of them. We then extend the discussion by modifying the relationship between the two angles, including multiplicative relations and fixed differences. Ultimately, we uncover connections between these loci and other well-known curves, and we explain the underlying geometric nature of these relationships.