Analytical Geometry

Chapter 9

Polar Coordinates

9.1  INTRODUCTION

A coordinate system represents a point in a plane by an ordered pair of numbers called coordinates. Earlier we used Cartesian coordinates which are directed distances from two perpendicular axes. Now we describe another coordinate system introduced by Newton called polar coordinates which is more convenient for some special purposes.

9.2  DEFINITION OF POLAR COORDINATES

We choose a point in the plane and it is called the pole (or origin) and is denoted by O. Then we draw a ray (half line) starting at O called polar axis. This is usually drawn horizontally to the right and corresponds to positive x-axis in Cartesian coordinates.

Let P be any point in the plane and r be the distance from O to P. Let ...