Analytical Geometry

Chapter 4

Circle

4.1  INTRODUCTION

Definition 4.1.1: A circle is the locus of a point in a plane such that its distance from a fixed point in the plane is a constant. The fixed point is called the centre of the circle and the constant distance is called the radius of the circle.

4.2  EQUATION OF A CIRCLE WHOSE CENTRE IS (h, k) AND RADIUS r

Let C (h, k) be the centre of the circle and P (x, y) be any point on the circle. CP = r is the radius of the circle. CP² = r² (i.e.) (x − h)² + (y − k)² = r². This is the equation of the required circle.

Note 4.2.1: If the centre of the circle is at the origin, then the equation of the circle is x² + y² = ...