Conic Sections

Conic Sections

Conic sections are graceful curves that can be defined in several ways and constructed by a wide variety of means. Most importantly, when a plane intersects a cone, the outline of a conic section results. This book will attempt the observation and manipulation of conic sections via their many definitions.

Contents

Types of Conic Sections

• General Conic Sections
• The Circle
• The Ellipse
• The Parabola
• The Hyperbola
• Lines and Points: Degenerate Conic Sections

Features of Conic Sections

• Foci of Conic Sections
• Conic Sections as Loci
• Eccentricity

Conic Sections as Algebraic Relations

• Intercepts of Conic Sections
• Translation of Axes
• Rotation of Axes
• Rotation of Axes (examples)
• Slopes of Conic Sections

Other Systems

• Conic Sections in Polar Coordinates
• Parametric Forms of Conic Sections

Example Problems

• The Ellipse
• The Parabola
• The Hyperbola
• Identifying Conics
• Rotating Conics

Conclusion

• Concluding Remarks
• Acknowledgements and Further Reading