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Analytical Geometry by P. R. Vittal

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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.) (xh)2 + (yk)2 = r2. This is the equation of the required circle.

Equation

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

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