## 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. *CP*^{2} = *r*^{2} (i.e.) (*x* − *h*)^{2} + (*y* − *k*)^{2} = *r*^{2}. 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 *x*^{2} + *y*^{2} = ...

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