Dave4Math / Courses / Topics in Analytic Geometry

Topics in Analytic Geometry

Master topics in analytic geometry. In these lessons, you'll learn conic sections, polar coordinates, and polar equations of conic sections. You'll get valuable experience using polar coordinates in this course, and you'll become a pro with conic sections.


January 11, 2021

Created by Dave

This course begins Summer 2021.
Current Status
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Did you know that RenĂ© Descartes created Analytic Geometry? You know, “I think; therefore I am.” and the Cartesian plane. Independently Pierre de Fermat also developed Analytic Geometry, and you should wonder without Analytic Geometry, would there be any calculus, any modern-day technology? Introducing Dave’s online math course: Topics in Analytic Geometry. This course begins your journey down a road where you end up developing …

Who This Course is For

  • Students in college who want to learn more mathematics.
  • Anyone interested in analytic geometry.
  • Students who are enrolled in precalculus and want to improve their grade.
  • Anyone interested in getting prepared for calculus 1.
  • Anyone wanting to learn about parabolas, circles, ellipses, hyperbolas, parametric equations, and polar coordinates.


There is no required textbook, though you will need an up-to-date web browser, paper, and pen. A hand-held scientific calculator of your choice is required.

What You’ll Learn in Topics in Analytic Geometry

  • Conics
  • Circles
  • Parabolas
  • Reflective Property of Parabolas
  • Ellipses
  • Eccentricity
  • Hyperbolas
  • Asymptotes of a Hyperbola
  • General Equations of Conics
  • Plane Curves
  • Sketching a Plane Curve
  • Eliminating the Parameter
  • Finding Parametric Equations for a Graph
  • Polar Coordinates
  • Coordinate Conversion
  • Equation Conversion
  • Graphs of Polar Equations
  • Symmetry
  • Zeros and Maximum r-Values
  • Special Polar Graphs
  • Alternative Definition of Conics
  • Polar Equations of Conics

Course Description

I recommend the prerequisite course Sequences and Series. If you’re not sure if this course is for you, checkout the course contents below or find out more by checking out my free precalculus articles.

Course Content

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David A. Smith

Mathematics Educator

I sincerely believe that the potential in every student can be unlocked. As an accomplished and dedicated instructor, I have firm confidence that I can provide significant value to your studies.

I relish teaching and use it as a channel for my creativity as I seek to deliver real-life and relevant connections between the mathematics that I teach and my students. Promoting an active learning environment and excitement about mathematics is my dream come true.

David Smith (Dave) has a B.S. and M.S. in Mathematics and has enjoyed teaching precalculus, calculus, linear algebra, and number theory at both the junior college and university levels for over 20 years. David is the founder and CEO of Dave4Math.