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

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Presentation transcript:

MATHPOWER TM 12, WESTERN EDITION Chapter 3 Conics

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

This is the of the equation of a circle with the centre at Developing the Standard Forms of 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 = r 2 Therefore, the equation of the circle in standard form is Finding the Equation of a Circle 3.3.4

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

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 Finding the Centre and the Radius

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

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 = Using a Graphing Calculator

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

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