1. Slide 10.1- 1 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. OBJECTIVES Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Conic Sections: Overview In this chapter, we study curves called conic sections. As the name implies, these curves are the sections of a cone (similar to an ice cream cone) formed when a plane intersects the cone. SECTION 10.1

3. Slide 10.1- 3 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley RIGHT CIRCULAR CONE Draw a circle on a flat surface. Draw a line called the axis, that passes through the center of the circle and is perpendicular to the flat surface. Choose a point above the flat surface on this line. The surface consisting of all the lines that simultaneously pass through both the point and the circle is called a right circular cone with vertex V. The vertex separates the surface into two parts called nappes of the cone.

4. Slide 10.1- 4 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley RIGHT CIRCULAR CONE

5. Slide 10.1- 5 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley CIRCLE If the slicing the plane is horizontal (parallel to the surface), then a circle is formed.

6. Slide 10.1- 6 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley ELLIPSE If the slicing the plane is inclined slightly from the horizontal, then an oval shaped curve called an ellipse is formed.

7. Slide 10.1- 7 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley PARABOLA If the slicing the plane is parallel to the “side” of the cone, then the curve formed is called a parabola.

8. Slide 10.1- 8 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley HYPERBOLA If the slicing the plane intersects both nappes of the cone, the resulting curve formed is called a hyperbola.

9. Slide 10.1- 9 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley DEGENERATE CONIC SECTIONS The point and lines obtained by a slicing plane through the vertex are called degenerate conic sections.