This concise guide, based on Tanner’s Brief Course in Analytic Geometry, presents how algebraic equations describe planes, surfaces, and curves in space. It explains how to use traces on coordinate planes to determine the nature of a surface, and how to visualize intersections, projections, and the formation of curves from pairs of surfaces. The book also covers surfaces of revolution, including cones, spheres, and spheroids, with practical examples to build intuition.

Readers will see how to convert complex equations into standard forms, learn the role of intercepts and normal forms, and follow step‑by‑step demonstrations that connect geometry to algebra. The material covers foundational topics like parabolas, ellipses, hyperbolas, and their special cases, with emphasis on interpretation and application rather than memorization.

How to recognize surfaces and curves from algebraic equations and their intersections.
Techniques for tracing surfaces on coordinate planes and using intercepts to deduce shape.
Standard forms and geometric properties of parabolas, ellipses, and hyperbolas, plus revolved surfaces.
Worked examples and exercises that build confidence in solving conic and quadric problems.

Ideal for students beginning analytic geometry or reviewing the fundamentals of conic sections and surface theory.

About the Author

JOSEPH P. ALLEN is President of the Robert C. Byrd National Technology Transfer Center at Wheeling Jesuit University in West Virginia. Allen has also served as the Director of the Office of Technology Commercialization at the U.S. Department of Commerce.

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