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2.1. CONIC SECTIONS
127
•
First, since
x
and
y
each enter Equation (
2.13
) only as their squares,
replacing
x
with
−
x
(or
y
with
−
y
) does not change the equation:
this means the curve is invariant under
refection across the
y
axis
. In particular, this gives us a second focus/directrix pair for
the curve:
F
(
ae,
0) and
x
=
a/e
.
•
Second, it is clear that the ellipse is bounded: in fact the curve has
x
intercepts (
±
a,
0) and
y
intercepts (0
,
±
b
). In the case
a > b
the
distance 2
a
(
resp
. 2
b
) between the
x
intercepts (
resp
.
y
intercepts) is
called the
major axis
(
resp
.
minor axis
); the corresponding
numbers
a
and
b
are the
semimajor axis
and the
semiminor
axis
,and the
x
intercepts are sometimes called the
vertices
of the
ellipse. When
a < b
, the names are interchanged. Equation (
2.13
)
with
b > a
can be regarded as obtained from a version with
b < a
by
interchanging
x
with
y
. Geometrically, this means that when
b > a
the foci are on the
y
axis instead of the
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus, Conic Sections

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