slide 10.1- 1 copyright © 2007 pearson education, inc. publishing as pearson addison-wesley

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

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

OBJECTIVES

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

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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.

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RIGHT CIRCULAR CONE

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CIRCLE

If the slicing the plane is horizontal (parallel to the surface), then a circle is formed.

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ELLIPSE

If the slicing the plane is inclined slightly from the horizontal, then an oval shaped curve called an ellipse is formed.

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PARABOLA

If the slicing the plane is parallel to the “side” of the cone, then the curve formed is called a parabola.

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HYPERBOLA

If the slicing the plane intersects both nappes of the cone, the resulting curve formed is called a hyperbola.

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DEGENERATE CONIC SECTIONSThe point and lines obtained by a slicing plane through the vertex are called degenerate conic sections.