1. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 12.2 - 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 12.2 - 2 Nonlinear Functions, Conic Sections, and Nonlinear Systems Chapter 12

3. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 12.2 - 3 12.2 The Circle and the Ellipse

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 4 12.2 The Circle and the Ellipse Objectives 1.Find the equation of a circle given the center and radius. 2.Determine the center and radius of a circle given its equation. 3.Recognize the equation of an ellipse. 4.Graph ellipses.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 5 12.2 The Circle and the Ellipse The Conic Sections – Circle and Ellipse Circle Ellipse

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 6 12.2 The Circle and the Ellipse The Circle x y

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 7 12.2 The Circle and the Ellipse Finding the Equation of a Circle and Graphing It

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 8 12.2 The Circle and the Ellipse Determine the Center and Radius of a Circle

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 9 12.2 The Circle and the Ellipse Determine the Center and Radius of a Circle

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 10 12.2 The Circle and the Ellipse Determine the Center and Radius of a Circle

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 11 12.2 The Circle and the Ellipse The Ellipse x y

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 12 12.2 The Circle and the Ellipse The Ellipse x y

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 13 12.2 The Circle and the Ellipse Graphing an Ellipse

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 14 12.2 The Circle and the Ellipse Graphing an Ellipse x y x

15. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 15 12.2 The Circle and the Ellipse Graphing an Ellipse with Horizontal and Vertical Shift

16. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 16 12.2 The Circle and the Ellipse Graphing an Ellipse with Horizontal and Vertical Shift