CHAPTER TWELVE - ANALYTIC GEOMETRY: THE CONIC SECTIONS

Abstract

This chapter highlights analytic geometry and its application. Analytic geometry combines the techniques of algebra with those of geometry. Analytic geometry enables the application of algebraic methods and equations to the solution of problems in geometry and, conversely, to obtain geometric representations of algebraic equations. The chapter presents a formula for the distance between two points and a formula for the coordinates of the midpoint of a line segment. With these as tools, the chapter presents the power of analytic geometry by proving a number of general theorems from plane geometry. The graphs of second-degree equations in two variables are known as the conic sections. The power of the methods of analytic geometry is well-demonstrated in a study of the conic sections. A geometric definition can be converted into an algebraic equation, and an algebraic equation can be classified by the type of graph it represents.