This document defines key terms related to circles: - A circle consists of all points equidistant from a fixed center point. - The radius is the fixed distance from the center point to any point on the circle. - A chord connects any two points on a circle. A diameter passes through the center and divides the circle into two equal halves. - The standard equation of a circle with center (h, k) and radius r is (x - h)2 + (y - k)2 = r2.

1. CIRCLE

2. GROUP MEMBERS:
NOOR KAMARIAH BINTI ALING
0914018
SITI ‘AQILAH BINTI MAHYIDDIN
0918878

3. A circle is defined as the collection of all the points on a plane that are at equal
distance from a given fixed point on the plane.
This fixed point is called centre of the circle and the fixed distance is called
the radius.
A line segment joining two points on the figure is a chord. The following are
examples of two chords.

4. -When a chord passes through the center,we call it a diameter. A
diameter usually divides such figure into two equal halves. Each half is
called a semi-circle
-Half a diameter is called a radius.
-In other words, 2 radii= diameter

5. CENTER AT THE ORIGIN
The circle with centre (0, 0) and radius r has the equation:
x2 + y2 = r2
This means any point (x, y) on the circle will be "true" when
substituted into the circle equation.

6. CENTER NOT AT THE ORIGIN
The circle with centre (h, k) and radius r has the equation:
(x − h)2 + (y − k)2 = r2

7. THE GENERAL FORM OF THE CIRCLE
An equation which can be written in the following form (with constants D, E,
F) represents a circle:
x2 + y2 + Dx + Ey + F = 0

8. Example:
Find the centre and radius of the circle
x2 + y2 + 8x + 6y = 0
Sketch the circle.
Answer:
Our aim is to get the equation into the form: (x − h)2 + (y − k)2 = r2
Group the x parts together and the y parts together:
Complete the square on each of the x and y parts.

9. This is now in the format we require and we can determine the center and
radius of the circle.
So the centre of the circle is (-4, -3) and the radius is 5 units.
Note that the circle passes through (0, 0). This is logical, since (-4)2 + (-3)2 = (5)2

10. Real life examples:
-bicycle wheels
- coins
-dimes and pennies
-CDs
-MP3 players.

11. REFERENCES
http://www.basic-mathematics.com/the-circle.html
http://www.intmath.com/plane-analytic-geometry/3-circle.php#general