Circle : Basic concept

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Circle : Basic concept

  1. 1. CIRCLE
  2. 2. GROUP MEMBERS: NOOR KAMARIAH BINTI ALING 0914018SITI ‘AQILAH BINTI MAHYIDDIN 0918878
  3. 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 calledthe radius. A line segment joining two points on the figure is a chord. The following are examples of two chords.
  4. 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. 5. 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.
  6. 6. CENTER NOT AT THE ORIGINThe circle with centre (h, k) and radius r has the equation: (x − h)2 + (y − k)2 = r2
  7. 7. 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
  8. 8. 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.
  9. 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. 10. Real life examples:-bicycle wheels- coins-dimes and pennies-CDs-MP3 players.
  11. 11. REFERENCEShttp://www.basic-mathematics.com/the-circle.htmlhttp://www.intmath.com/plane-analytic-geometry/3-circle.php#general

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