M408M Learning Module Pages
Main page

Chapter 10: Parametric Equations and Polar Coordinates

Learning module LM 10.1: Parametrized Curves:

Learning module LM 10.2: Calculus with Parametrized Curves:

Learning module LM 10.3: Polar Coordinates:

Learning module LM 10.4: Areas and Lengths of Polar Curves:

Learning module LM 10.5: Conic Sections:

Learning module LM 10.6: Conic Sections in Polar Coordinates:

      Foci and directrices
      Visualizing eccentricity
      Polar equations for conic sections
      Astronomy

Chapter 12: Vectors and the Geometry of Space

Chapter 13: Vector Functions

Chapter 14: Partial Derivatives

Chapter 15: Multiple Integrals

Visualizing eccentricity

Visualizing Ellipticity

Use the interactive figure to the right to generate conic sections with a focus at the origin. You can vary the distance $d$ to the directrix, the eccentricity $e$, and the rotation angle $\theta$ (called $\theta_0$ in subsequent slides). What happens when the eccentricity crosses through 1?