MA 15400
Lesson 27
Section 11.2
Ellipses
1
An
ellipse
is the set of all points in a plane, the sum 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 ellipse.
The center
C
of the above ellipse is
marked.
There are two axes:
The
major axis
is the longer of the two and contains the foci.
Its endpoints
are the
vertices
of the ellipses.
The
minor axis
is the shorter of the two and its endpoints are
simply known as the endpoints of the minor axis.
There are three important numbers associated with an ellipse:
a, b,
and
c
.
These numbers
correspond the distances involving the center, the foci, the vertices, and the endpoints of the
minor axis.
Points
and
F
F
′
are the foci
(plural of focus).
The sum of
the distances from any point of
an ellipse (such as
P
or
H
) to
each focus is a constant value.
For example, if
10, then
10
FP
F P
FH
F H
′
+
=
′
+
=
.
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 Spring '08
 DELWORTH
 Algebra, Trigonometry, Distance, Semiminor axis, eccentricity

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