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6. (a)
[
2
6, 6] by [
2
4, 4]
The graph is a circle of radius 2 centered at (
h
, 0). As
h
changes, the graph shifts horizontally.
(b)
[
2
6, 6] by [
2
4, 4]
The graph is a circle of radius 2 centered at (0,
k
). At
k
changes, the graph shifts vertically.
(c)
Since the circle is to be centered at (2,
2
3), we use
h
5
2 and
k
52
3. Since a radius of 5 is desired, we
need to change the coefficients of cos
t
and sin
t
to 5.
x
5
5 cos
t
1
2,
y
5
5 sin
t
2
3, 0
#
t
#
2
p
(d)
x
5
5 cos
t
2
3,
y
5
2 sin
t
1
4, 0
#
t
#
2
p
7. (a)
[
2
3, 3] by [
2
2, 2]
Initial point: (1, 0)
Terminal point: (
2
1, 0)
(b)
x
2
1
y
2
5
cos
2
t
1
sin
2
t
5
1
The parametrized curve traces the upper half of the
circle defined by
x
2
1
y
2
5
1 (or all of the semicircle
defined by
y
5
ˇ
1
w
2
w
x
w
2
w
).
8. (a)
[
2
3, 3] by [
2
2, 2]
Initial and terminal point: (0, 1)
(b)
x
2
1
y
2
5
sin
2
(2
p
t
)
1
cos
2
(2
p
t
)
5
1
The parametrized curve traces all of the circle defined
by
x
2
1
y
2
5
1.
9. (a)
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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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