MA 15400
Lesson 29
Section 11.3
Hyperbolas
1
A
hyperbola
is the set of all points in a plane, the
difference
of whose distances from two fixed
points (the
foci
) in the plane is a positive constant.
The midpoint of the two foci is the
center
of the hyperbola.
(Centers are marked with C.)
The
foci are
c
units
from the center.
The points where the hyperbola intersects the line joining the foci are the
vertices
.
The vertices
are
a
units
from the center.
In a hyperbola
c
>
a
, where in an ellipse
a
>
c
.
There are two axes:
1) The line segment V'V is the
transverse axis
.
The foci lie beyond the endpoints of the
transverse axis.
The length of a transverse axis is 2
a
.
2)
The graph does not cross the other axis, the
conjugate axis
.
Its endpoints, W and W',
are not points on the hyperbola, however, are very important in creating an auxiliary
rectangle that assists in sketching the graph.
The length of a conjugate axis is 2
b
.
(See the next page.)
There are two ‘branches’ of a
hyperbola.
If the foci are on
a horizontal line, the
‘branches’ are opening left
and right.
If the foci are on a
vertical line, the ‘branches’
are opening up and down.
The foci will lie ‘inside’ the
‘branches’.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 DELWORTH
 Algebra, Trigonometry, ax, transverse axis

Click to edit the document details