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Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 12.2 - 1
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Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 12.2 - 1
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 12.2 - 2
Nonlinear Functions, Conic Sections,
and Nonlinear Systems
Chapter 12
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 12.2 - 3
12.2
The Circle and the Ellipse
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.
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
CircleEllipse
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 6
12.2 The Circle and the Ellipse
The Circle
x
y
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
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
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
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
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 11
12.2 The Circle and the Ellipse
The Ellipse
x
y
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 12
12.2 The Circle and the Ellipse
The Ellipse
x
y
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 12.2 - 13
12.2 The Circle and the Ellipse
Graphing an Ellipse
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
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
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
