LESSON NOTES MENU
 
Course: College Algebra
Topic: Conic Sections
Subtopic: Hyperbolas

Overview

One of the conic section curves is the hyperbola. A hyperbola has two "branches" and is created by slicing a "double cone" (one atop the other touching at their vertices) by a plane to create the two branches. The curve of a hyperbola looks somewhat like a parabola but it is not the same curve at all! A hyperbola is bounded by intersecting asymptote lines, but a parabola is unrestrained. This changes the way the hyperbola curve grows in subtle but important ways. The reflective properties of the hyperbola are distinct from those of a parabola (important difference to note!). In comparison to an ellipse, the definition of the hyperbola differs from the definition of the ellipse in terms of distance from the foci to points on the curve.

Objectives

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

Terminology

Terms you should be able to define: ellipse, standard form, focal points (foci), vertices, transverse axis, conjugate axis, defining rectangle, asymptote lines, branches, eccentricity.

Formulae: You should know how to use these formulae!


Supplemental Resources (recommended)

Read Importance of Hyperbolas in Life for a brief overview of applications from Sciencing.

Explore the interactive graphs at Interactive Hyperbola Graphs which show how the hyperbola's focal points form the hyperbola's two branches.

Supplemental Resources (optional)

If you need supplemental tutorial videos with examples relevant to this section go to James Sousa's MathIsPower4U and search for topics: "Graphing and Writing Equations of Hyperbolas".

The Hyperbola has lots of examples if you need more practice working with equations and graphs of hyperbolas.

rev. 2020-11-29