Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: College Algebra
Topic: Conic Sections
Subtopic: Introduction to Conics

Overview

The conic sections are curves formed when a cone is sliced by a plane (see your text for pictures). Depending on the angle of the plane in relation to the cone, the curve formed at their intersection is an ellipse, parabola, or hyperbola. (A circle is usually also included in this list, but actually a circle is just a special case of an ellipse.) We will study these static curves in preparation for calculus III where we will study the motion of these curves (including in polar form). The conics have lots of real-life applications including parabolic trajectories, elliptical orbits of the planets, and the reflective properties of hyperbolas.

Objectives

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

• 7.1.1 Name the three conic section curves and know how they are formed by slicing a cone
• 7.1.2 Know some real-life applications of each conic section

Terminology

Terms you should be able to define: cone, section, slice, conic section

Supplemental Resources

Watch Introduction to Conic Sections from MathIsPower4U.

Read Occurrence of the Conics for a nice overview of conic sections and their applications.

rev. 2020-11-29