GROUP MEMBERS: NOOR KAMARIAH BINTI ALING 0914018SITI ‘AQILAH BINTI MAHYIDDIN 0918878
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 calledthe radius. A line segment joining two points on the figure is a chord. The following are examples of two chords.
-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
CENTER AT THE ORIGINThe circle with centre (0, 0) and radius r has the equation: x2 + y2 = r2This means any point (x, y) on the circle will be "true" whensubstituted into the circle equation.
CENTER NOT AT THE ORIGINThe circle with centre (h, k) and radius r has the equation: (x − h)2 + (y − k)2 = r2
THE GENERAL FORM OF THE CIRCLEAn equation which can be written in the following form (with constants D, E,F) represents a circle: x2 + y2 + Dx + Ey + F = 0
Example:Find the centre and radius of the circlex2 + y2 + 8x + 6y = 0Sketch the circle.Answer:Our aim is to get the equation into the form: (x − h)2 + (y − k)2 = r2Group the x parts together and the y parts together: Complete the square on each of the x and y parts.
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
Real life examples:-bicycle wheels- coins-dimes and pennies-CDs-MP3 players.