4.
0
#
t
# }
p
2
}
:
[
2
6, 6] by [
2
4, 4]
0
#
t
#
p
:
[
2
6, 6] by [
2
4, 4]
0
#
t
# }
3
2
p
}
:
[
2
6, 6] by [
2
4, 4]
0
#
t
#
4
p
:
[
2
6, 6] by [
2
4, 4]
Let
d
be the length of the parametric interval. If
d
,
2
p
,
you get
}
2
d
p
}
of a complete ellipse. If
d
5
2
p
, you get the
complete ellipse. If
d
.
2
p
, you get the complete ellipse
but portions of the ellipse will be traced out more than
once. For example, if
d
5
4
p
the entire ellipse is traced
twice.
5.
0
#
t
#
2
p
:
[
2
6, 6] by [
2
4, 4]
initial point: (5, 0)
terminal point: (5, 0)
p
#
t
#
3
p
:
[
2
6, 6] by [
2
4, 4]
initial point: (
2
5, 0)
terminal point: (
2
5, 0)
}
p
2
}
#
t
# }
3
2
p
}
:
[
2
6, 6] by [
2
4, 4]
initial point: (0,
2
2)
terminal point: (0, 2)
Each curve is traced clockwise from the initial point to the
terminal point.
Exploration 3
Graphing the Witch of Agnesi
1.
We used the parameter interval [0,
p
] because our graphing
calculator ignored the fact that the curve is not defined
when
t
5
0 or
p
. The curve is traced from right to left
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN

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