Download presentation

Presentation is loading. Please wait.

Published byAlyssa Garrett Modified over 3 years ago

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

2
**Developing the Standard Forms of the Equation of a Circle**

Note: OP is the radius of the circle. P(x, y) O(0, 0) The standard form of the equation of a circle with its centre at the origin (0, 0) is x2 + y2 = r2. 3.3.2

3
**Developing the Standard Forms of the Equation of a Circle**

P(x, y) C(h, k) This is the standard form of the equation of a circle with the centre at (h, k). 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). (h, k) (x, y) From the general form: (x - h)2 + (y - k)2 = r2 Substitute the values of h and k from C(-5, 2): (x - (-5))2 + (y - 2)2 = r2 (x + 5)2 + (y - 2)2 = r2 (x + 5)2 + (y - 2)2 = r2 (-8 + 5)2 + (7 - 2)2 = r2 = r2 34 = r2 Use the point P(-8, 7) to find the value of r2: Therefore, the equation of the circle in standard form is (x + 5)2 + ( y - 2)2 = 34. 3.3.4

5
**Writing the General Form of the Equation of a Circle**

The general form of the equation is Ax2 + Cy2 + Dx + Ey + F = 0. Write the following equation in general form: (x + 5)2 + (y - 2)2 = 34 (x + 5)2 + (y - 2)2 = 34 x2 + 10x y2 - 4y + 4 = 34 x2 + y2 + 10x - 4y + 29 = 34 x2 + y2 + 10x - 4y - 5 = 0 3.3.5

6
**Finding the Centre and the Radius**

Find the centre and the radius of each circle: 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 (x2 - 8x + _____ ) + (y2 + 10y + _____) = 14 + _____ + _____ 16 25 16 25 (x - 4)2 + (y + 5)2 = 55 The centre is (4, -5) and the radius is 7.4. x2 + 3y2 + 6x + 12y + 5 = 0 (3x2 + 6x) + (3y y) = -5 3(x2 + 2x + _____) + 3(y2 + 4y + _____) = -5 + _____ + _____ 1 4 3 12 3(x + 1)2 + 3(y + 2)2 = 10 The centre is (-1, -2) 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: Circle (3, 4, 4) 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 x2 + y2 = 16 Ax2 + y2 = 16, when A = 0 x2 + y2 = 16 x2 + y2 = 16 x2 + y2 = 16 4x2 + y2 = 16 0.5x2 + y2 = 16 4x2 + y2 = 16 0.5x2 + y2 = 16 4x2 + y2 = 16 3.3.8

9
**Using a Graphing Calculator [cont’d]**

Using your graphing calculator, graph the following equations: d) x2 + 4y2 = 16 e) x y2 = 16 f) x2 + Cy2 = 16, when C = 0 x2 + Cy2 = 16, when C = 0 x2 + y2 = 16 x2 + y2 = 16 x2 + y2 = 16 x2 + 4y2 = 16 x2 + 4y2 = 16 x2 + 4y2 = 16 x y2 = 16 x y2 = 16 3.3.9

10
**Using a Graphing Calculator [cont’d]**

Conclusions: The values of A and C affect the graph of the circle by either a vertical or horizontal compression or expansion: A > 1 results in a horizontal compression. 0 < A < 1 results in a horizontal expansion. A = 0 results in a pair of horizontal parallel lines. C > 1 results in a vertical compression. 0 < C < 1 results in a vertical expansion. C = 0 results in a pair of vertical parallel lines. 3.3.10

11
**Assignment Suggested Questions: Pages 141 and 142 A 1-25 odd, 27-32**

B , 49, 50, 51, 54, 56, 58 (graph), 62 3.3.11

Similar presentations

Presentation is loading. Please wait....

OK

口算小能手.

口算小能手.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on indian premier league Ppt on water conservation download Ppt on morbid obesity and anaesthesia Ppt on complex numbers class 11th physics Ppt on media and networking Ppt on college management system project Ppt on congruent triangles Ppt on power system transients Ppt on instrument landing system images Slides for ppt on pollution control