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The Circle

Chapter 3 Conics. 3.3. The Circle. 3.3. 1. MATHPOWER TM 12, WESTERN EDITION. Developing the Standard Forms of the Equation of a Circle. Note:. The standard form of the equation of a circle with its centre at the origin (0, 0) is. 3.3. 2.

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The Circle

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  1. Chapter 3 Conics 3.3 The Circle 3.3.1 MATHPOWERTM 12, WESTERN EDITION

  2. Developing the Standard Forms of the Equation of a Circle Note: The standard form of the equation of a circle with its centre at the origin (0, 0) is 3.3.2

  3. Developing the Standard Forms of the Equation of a Circle This is the of the equation of a circle with the centre at 3.3.3

  4. Finding the Equation of a Circle Determine the equation of a circle with centre C(-5, 2) and passing through the point P(-8, 7). From the standard form: (x - h)2 + (y - k)2 = r2 Therefore, the equation of the circle in standard form is 3.3.4

  5. Writing the General Form of the Equation of a Circle The general form of the equation is Write the following equation in general form: (x + 5)2 + (y - 2)2 = 34 3.3.5

  6. Finding the Centre and the Radius Find the centre and the radius of each circle: 1.x2 + y2 - 8x + 10y - 14 = 0 To find the centre and radius, write the equation in standard form. To do this, you must complete the square: x2 + y2 - 8x + 10y - 14 = 0 The centre is and the radius is 2.3x2 + 3y2 + 6x + 12y + 5 = 0 The centre is and the radius is 3.3.6

  7. Using a Graphing Calculator Graph: (x - 3)2 + (y - 4)2 = 16 Your calculator will only graph a function, therefore, you must write the equation in the form y = . Make sure that you use a ZSquare graphing window. You can also use the Draw circle command on your TI-83: Press [2nd][PRGM] 9 and enter the following: 3.3.7

  8. Using a Graphing Calculator Using your graphing calculator, graph the following equations: a) x2 + y2 = 16 b) 4x2 + y2 = 16 c) 0.5x2 + y2 = 16 d) Ax2 + y2 = 16, when A = 0 3.3.8

  9. Using a Graphing Calculator [cont’d] Using your graphing calculator, graph the following equations: d) x2 + 4y2 = 16 e) x2 + 0.5y2 = 16 f) x2 + Cy2 = 16, when C = 0 3.3.9

  10. Assignment Suggested Questions: Pages 141 and 142 A 1-25 odd, 27-32 B 36-45, 49, 50, 51, 54, 56, 58 (graph), 62 3.3.11

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