This document discusses the equation of a hyperbola and provides examples. It begins by presenting the standard equation of a hyperbola with center (0,0) and foci at (-c,0) and (c,0). It then gives an example of a hyperbola with its foci and asymptotes labeled. The next section works through an example problem of finding the equation of a hyperbola given its vertices and the endpoints of its conjugate axis. The document concludes by recapping the standard form equation that was derived.

1. 10.3 Hyperbola.notebook December 01, 2010
hyperbola
An equation of the hyperbola
with center (0, 0) and foci at (-c, 0) and (c, 0) is
x2 - y2 = 1
a2 b2
where c2 = a2 + b2
and whose asymptotes are located at:
y = (+ b/a)x
(think rise over run!)
Dec 1­12:44 PM
1

2. 10.3 Hyperbola.notebook December 01, 2010
Example
Focus pt
Focus pt
Dec 1­1:02 PM
2

3. 10.3 Hyperbola.notebook December 01, 2010
Example 2
Find an equation of the hyperbola with vertices at (1,0) and (­5,0) and the
endpoints of its conjugate axis at (­2,­2) and (­2,2).
The vertices indicate that the hyperbola would have an equation in standard
form as given below.
The center will be midway between the vertices at (­2,0). The distance
between the vertices is 2a and equals 6 so a = 3. The length of the conjugate
axis is 2b and equals 4 so b = 2. Thus the equation of the hyperbola in
standard form is
Dec 1­2:28 PM
3

4. 10.3 Hyperbola.notebook December 01, 2010
Dec 1­2:39 PM
4