A Comparative Study of Graphical and Analytical Methods for Constructing the Hyperbola with an Application-Oriented Approach

Abstract

Hyperbola is one of the conic sections that has wide applications in various fields, including mathematics, geometry, medicine, and also in the design of bridges and towers. For this reason, it has always been of interest and use by scientists in the fields of mathematics and engineering since ancient times. The aim of this research is to compare different methods of drawing hyperbola and examine its applications. This research was conducted using a library method and using new, reliable scientific and international sources. In this research, four drawing methods (centripetal, asymptotic, arc intersection, and analytical method) were compared with each other, and each of these methods was examined in terms of accuracy, ease of implementation, advantages, and limitations. The findings and results of the research show that the analytical and centripetal methods have the highest accuracy in drawing hyperbola, because they are based on mathematical equations and geometric principles. In contrast, the methods (asymptote and arc intersection) are more suitable for practical applications and approximate drawings due to their simplicity; but they are less accurate; especially the arc intersection method, which is more used or applicable for quick and practical drawings.