Geometric Foundations of Engineering Design: The Role of Conic Sections Enhanced by Artificial Intelligence

Many branches of engineering rely on four fundamental geometric shapes: circle, ellipse, parabola, and hyperbola, whose intrinsic properties enable engineers to develop more accurate mathematical models, optimize trajectories, and enhance structural integrity in complex design contexts. This study examines how these classical conic sections are applied in real-world engineering problems and explores the utilization of geometric principles in robotics, signal processing, and automated systems to support efficient problem-solving. By relating the properties of conic sections to engineering requirements in areas such as bridge design, trajectory optimization, and structural analysis, the study elucidates how these forms underpin both analytical modelling and practical implementation in contemporary engineering practice. The analysis shows that the relevance of conic sections to practical engineering applications is clearly demonstrated across multiple domains, highlighting their role in improving modelling accuracy, guiding system optimization, and informing robust design strategies. The study concludes that classical geometry, particularly the theory of conic sections, continues to play a vital role in shaping modern engineering practices and carries important implications for advancing engineering education, promoting interdisciplinary integration, and sustaining innovation in technology and infrastructure development.