Unveiling New Insights into the Geometry of the Parabola

This research article explores the geometric and mathematical significance of the parabola; a fundamental conic section defined as the locus of a point whose distance from a fixed point (focus) and a fixed line (directrix) are equal. Moving beyond its classical definition, the study introduces a set of one hundred newly derived theorems concerning the tangent, normal, sub-tangent, sub-normal and focus of the parabola. Each theorem is rigorously developed with detailed proofs, step-by-step derivations, and illustrative diagrams to aid comprehension. In addition, the article presents a further 100 original theorems that establish precise mathematical relationships between the tangent, normal, focus, and other essential elements of the parabola. A preamble provides the fundamental formulas necessary for the derivations. Collectively, these contributions expand the theoretical framework of parabola geometry and serve as a significant reference for scholars engaged in advanced studies of conic sections and related fields.