LESSON NOTES MENU
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
Course: Calculus II
Topic: Parametric, Polar, and Conic Curves
Subtopic: Polar Equations of Conic Sections

Overview

Start by reviewing conic sections from a pre-calculus course. See Lesson Notes - College Algebra: Introduction to Conics | Parabolas | Ellipses | Hyperbolas | General & Degenerate Conics but ignore any "text notes". Work conics that are centered at the origin as well as those translated away from the origin.

Our main goal in this lesson is to concentrate performing calculus on the conic sections. Many calculus operations are simplified by converting the equations of the conics from rectangular form to polar form. This transformation is accomplished through an ingenious formula. We can then apply calculus to the polar form to find the area inside a bounded conic, the arc length of the conic, etc. Study conics that have horizontal or vertical axes as well as those that have a rotated axis.

Objectives

By the end of this topic you should know and be prepared to be tested on:

Terminology

Define: focal point, major and minor axes, directrix, pole, eccentricity, Kepler and his laws

Supplemental Resources (recommended)

Clark Math Dept's Conic Sections Formula Sheet reviews the standard and general conic section formulae from a precalculus course.

Explore the connection between eccentricity and conics via the java applet at www.mathwords.com/multimedia/Conics%20defined%20by%20eccentricity.htm

Supplemental Resources (optional)

These are both quite good reads. The first reviews concepts from Pre-Calculus and the second covers Calculus concepts.

Lesson: Conic Sections, Dale Hoffman's Contemporary Calculus

Lesson: Properties of the Conic Sections, Dale Hoffman's Contemporary Calculus