circle : basic concept
Post on 11-Sep-2014
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CIRCLE
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GROUP MEMBERS:
NOOR KAMARIAH BINTI ALING0914018
SITI ‘AQILAH BINTI MAHYIDDIN0918878
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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.
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-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
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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.
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CENTER NOT AT THE ORIGIN
The circle with centre (h, k) and radius r has the equation:
(x − h)2 + (y − k)2 = r2
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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
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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 = r2
Group the x parts together and the y parts together:
Complete the square on each of the x and y parts.
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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
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Real life examples:-bicycle wheels- coins-dimes and pennies-CDs-MP3 players.
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http://www.basic-mathematics.com/the-circle.html
http://www.intmath.com/plane-analytic-geometry/3-circle.php#general
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