1. MATHPOWER TM 12, WESTERN EDITION 3.3.1 3.3 Chapter 3 Conics

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

4. 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 = r 2 Therefore, the equation of the circle in standard form is Finding the Equation of a Circle 3.3.4

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

6. Find the centre and the radius of each circle: 1. x 2 + y 2 - 8x + 10y - 14 = 0 x 2 + y 2 - 8x + 10y - 14 = 0 To find the centre and radius, write the equation in standard form. To do this, you must complete the square: The centre is and the radius is 2. 3x 2 + 3y 2 + 6x + 12y + 5 = 0 The centre is and the radius is 3.3.6 Finding the Centre and the Radius

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 your graphing calculator, graph the following equations: a) x 2 + y 2 = 16 b) 4x 2 + y 2 = 16 c) 0.5x 2 + y 2 = 16 d) Ax 2 + y 2 = 16, when A = 0 3.3.8 Using a Graphing Calculator

9. d) x 2 + 4y 2 = 16 e) x 2 + 0.5y 2 = 16 f) x 2 + Cy 2 = 16, when C = 0 Using a Graphing Calculator [cont’d] 3.3.9 Using your graphing calculator, graph the following equations:

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