4.
[
2
9, 9] by [
2
6, 6]
(a)
1
2
3 cos
}
5
6
p
}
,
2
3 sin
}
5
6
p
}
2
5
1
}
3
ˇ
2
3
w
}
,
2
}
3
2
}
2
(b)
1
5 cos
1
tan
2
1
1
}
4
3
}
22
, 5 sin
1
tan
2
1
1
}
4
3
}
222
5
(3, 4)
(c)
(
2
1 cos 7
p
,
2
1 sin 7
p
)
5
(1, 0)
(d)
1
2
ˇ
3
w
cos
}
2
3
p
}
, 2
ˇ
3
w
sin
}
2
3
p
}
2
5
(
2
ˇ
3
w
, 3)
5.
[
2
6, 6] by [
2
4, 4]
(a)
r
5
ˇ
(
2
w
1
w
)
2
w
1
w
1
w
2
w
5
ˇ
2
w
, tan
u
5
}
2
1
1
}
5 2
1 with
u
in
quadrant II. The coordinates are
1
ˇ
2
w
,
}
3
4
p
}
2
.
1
ˇ
2
w
,
2
}
5
4
p
}
2
also works, since
r
is the same and
u
differs by 2
p
.
(b)
r
5
ˇ
1
w
2
w
1
w
(
w
2
w
ˇ
w
3
w
w
)
2
w
5
2, tan
u
5 2
}
ˇ
1
3
w
}
5 2
ˇ
3
w
with
u
in quadrant IV. The coordinates are
1
2,
2
}
p
3
}
2
.
1
2
2,
}
2
3
p
}
2
also works, since
r
has the opposite sign and
u
differs by
p
.
(c)
r
5
ˇ
0
w
2
w
1
w
3
w
2
w
5
3, tan
u
5
}
3
0
}
is undefined with
u
on
the positive
y
axis. The coordinates are
1
3,
}
p
2
}
2
.
1
3,
}
5
2
p
}
2
also works, since
r
is the same and
u
differs by 2
p
.
(d)
r
5
ˇ
(
2
w
1
w
)
2
w
1
w
0
w
2
w
5
1, tan
u
5
}
2
0
1
}
5
0 with
u
on the
negative
x
axis. The coordinates are (1,
p
). (
2
1, 0) also
works, since
r
has the opposite sign and
u
differs by
p
.
6.
[
2
9, 9] by [
2
6, 6]
(a)
r
5
ˇ
(
2
w
ˇ
w
3
w
w
)
2
w
1
w
(
w
2
w
1
w
)
2
w
5
2, tan
u
5
}
2
2
ˇ
1
3
w
}
5
}
ˇ
1
3
w
}
with
u
in quadrant III. The coordinates are
1
2,
}
7
6
p
}
2
.
1
2
2,
}
p
6
}
2
also works, since
r
has the opposite sign and
u
differs by
p
.
(b)
r
5
ˇ
3
w
2
w
1
w
4
w
2
w
5
5, tan
u
5
}
4
3
}
with
u
in quadrant I.
The coordinates are
1
5, tan
2
1
}
4
3
}
2
.
1
2
5,
p
1
tan
2
1
}
4
3
}
2
also works, since
r
has the opposite sign and
u
differs
by
p
.
(c)
r
5
ˇ
0
w
1
w
(
w
2
w
2
w
)
2
w
5
2, tan
u
5 2
}
2
0
}
is undefined with
u
on the negative
y
axis. The coordinates are
1
2,
}
3
2
p
}
2
.
1
2,
2
}
p
2
}
2
also works, since
r
is the same and
u
differs
by 2
p
.
(d)
r
5
ˇ
2
w
2
w
1
w
0
w
2
w
5
2, tan
u
5
}
0
2
}
5
0 with
u
on the
positive
x
axis. The coordinates are (2, 0). (2, 2
p
) also
works, since
r
is the same and
u
differs by 2
p
.
7.
[
2
6, 6] by [
2
4, 4]
8.
[
2
6, 6] by [
2
4, 4]
9.
[
2
3, 3] by [
2
2, 2]
10.
[
2
3, 3] by [
2
2, 2]
Section 10.5
421
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11.
[
2
9, 9] by [
2
6, 6]
12.
[
2
6, 6] by [
2
4, 4]
13.
[
2
3, 3] by [
2
2, 2]
14.
[
2
3, 3] by [
2
2, 2]
15.
[
2
3, 3] by [
2
2, 2]
16.
[
2
3, 3] by [
2
2, 2]
17.
[
2
1.8, 1.8] by [
2
1.2, 1.2]
18.
[
2
3, 3] by [
2
2, 2]
19.
y
5
r
sin
u
, so the equation is
y
5
0, which is the
x
axis.
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 Spring '08
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 3 sec, 2k, 0 K, hyperbola., parabola.

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