Goals and Objectives of the
Cone Module

After completing this module you will be able to: describe that a double-napped cone is created when a line is rotated around a fixed point. identify the generator, vertex, and vertical axis of a double-napped cone. describe or show how to slice the double-napped cone to create circles, ellipses, parabolas, hyperbolas, and each of the degenerate conics. describe what happens to a circle as a horizontal plane cutting the double-napped cone moves towards and away from the cone's vertex. describe what happens to an ellipse as an inclined plane cutting the double-napped cone becomes more parallel and more perpendicular to the cone's vertical axis. describe what happens to a hyperbola as a plane cutting both naps of a double-napped cone moves closer and farther away from the cone's vertex. describe what happens to a parabola as a plane intersecting parallel to the generator of the double-napped cone moves closer and farther way from the cone's vertex. describe or show how the degenerate conics relate to the conic sections. describe that each of the conic sections and degenerate conics can be described by the general equation Ax2 + By2 + Cx + Dy + F = 0.