Section 9.3: The Ellipse
Instructor: Ms. Hoa Nguyen
([email protected])
1
Ellipse Definition
Definition of an Ellipse
:
Given any POSITIVE constant 2
a
and two fixed points
F
1
, F
2
(
foci
), the set of all points
P
such that
d
(
P, F
1
) +
d
(
P, F
2
) = 2
a
is called an
ellipse
.
Note:
d
(
A, B
) denotes the distance from
A
to
B
:
d
(
A, B
) =
(
x
A

x
B
)
2
+ (
y
A

y
B
)
2
.
The line containing the foci
F
1
, F
2
is called the
major axis
.
The midpoint of the line segment joining the foci is called the
center
of the ellipse.
The line through the center and perpendicular to the major axis is called the
minor
axis
.
The 2 points where the ellipse intersects the major axis are the vertices,
V
1
, V
2
of the
ellipse.
2
Find the Equation of the Ellipse
1
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Case 1: Major axis is the
x
axis, and the center is at the origin.
An equation of the ellipse whose
•
Major axis is the
x
axis.
•
The center is at the origin.
•
The foci are
F
1
= (

c,
0) and
F
2
= (
c,
0).
•
The vertices are
V
1
= (

a,
0) and
V
2
= (
a,
0).
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 Spring '11
 Nuegyen
 Euclidean geometry, Line segment, Ms. Hoa Nguyen

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