SS2 Third Term Further Mathematics Lesson Note – The Circle I

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WEEK ONE

CONIC-SECTION: THE CIRCLE 1

CONTENT

(a) Definition of circle

(b) Equation of Circle Given Centre and Radius

(c) General Equation of a Circle

SUB TOPIC: DEFINITION OF A CIRCLE

A circle is the set of all points in a plane at a fixed positive distance (radius) from a fixed point (centre).

A circle is also a plane curve which is the locus of a point which moves at a fixed distance from a fixed point.

The fixed distance is called the radius of the circle while the fixed point is called the centre of the circle.

SUB TOPIC: EQUATION OF A CIRCLE OF GIVEN CENTRE AND RADIUS.

The standard form for an equation of a circle is a direct consequence of the definition and length formula.

Let the centre of the circle be at a fixed point C (h,k) and the length of the radius be equal to r. Then if P (x_, y) be the moving point on the circle, we have by definition.

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