8 - ANALYTIC GEOMETRY: THE CONIC SECTIONS

Abstract

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. This chapter presents a formula for the coordinates of the midpoint of a line segment. It also explains how a geometric definition can be converted into an algebraic equation and how an algebraic equation can be classified by the type of graph it represents. A geometric figure defined as a set of points can often be described analytically by an algebraic equation. A circle is the set of all points in a plane that are at a given distance from a fixed point. The fixed point is called the center of the circle and the given distance is called the radius. The chapter presents the standard form of the equation of a circle. Given a fixed point, called the focus, and a fixed line, called the directrix, a parabola is the set of all points each of which is equidistant from the point and from the line.