447
CHAPTER 11
Analytic Geometry in Calculus
EXERCISE SET 11.1
1.
(1,
6
)
(3,
3
)
(4,
e
)
(–1,
r
)
0
p
/
2
(5,
8
)
(–6, –
p
)
2.
(
,
L
)
3
2
0
p
/
2
(
–
3,
i
)
(
–
5,
@
)
(2,
$
)
(0,
c
)
(2,
g
)
3.
(a)
(3
√
3
,
3)
(b)
(
−
7
/
2
,
7
√
3
/
2)
(c)
(3
√
3
,
3)
(d)
(0
,
0)
(e)
(
−
7
√
3
/
2
,
7
/
2)
(f)
(
−
5
,
0)
4.
(a)
(
−
4
√
2
,
−
4
√
2)
(b)
(7
√
2
/
2
,
−
7
√
2
/
2)
(c)
(4
√
2
,
4
√
2)
(d)
(5
,
0)
(e)
(0
,
−
2)
(f)
(0
,
0)
5.
(a)
both (5
, π
)
(b)
(4
,
11
π/
6)
,
(4
,
−
π/
6)
(c)
(2
,
3
π/
2)
,
(2
,
−
π/
2)
(d)
(8
√
2
,
5
π/
4)
,
(8
√
2
,
−
3
π/
4)
(e)
both (6
,
2
π/
3)
(f)
both (
√
2
, π/
4)
6.
(a)
(2
,
5
π/
6)
(b)
(
−
2
,
11
π/
6)
(c)
(2
,
−
7
π/
6)
(d)
(
−
2
,
−
π/
6)
7.
(a)
(5
,
0
.
6435)
(b)
(
√
29
,
5
.
0929)
(c)
(1
.
2716
,
0
.
6658)
8.
(a)
(5
,
2
.
2143)
(b)
(3
.
4482
,
2
.
6260)
(c)
(
4 +
π
2
/
36
,
0
.
2561)
9.
(a)
r
2
=
x
2
+
y
2
= 4; circle
(b)
y
= 4; horizontal line
(c)
r
2
= 3
r
cos
θ
,
x
2
+
y
2
= 3
x
, (
x
−
3
/
2)
2
+
y
2
= 9
/
4; circle
(d)
3
r
cos
θ
+ 2
r
sin
θ
= 6, 3
x
+ 2
y
= 6; line
10.
(a)
r
cos
θ
= 5,
x
= 5; vertical line
(b)
r
2
= 2
r
sin
θ
,
x
2
+
y
2
= 2
y
,
x
2
+ (
y
−
1)
2
= 1; circle
(c)
r
2
= 4
r
cos
θ
+ 4
r
sin
θ, x
2
+
y
2
= 4
x
+ 4
y,
(
x
−
2)
2
+ (
y
−
2)
2
= 8; circle
(d)
r
=
1
cos
θ
sin
θ
cos
θ
,
r
cos
2
θ
= sin
θ
,
r
2
cos
2
θ
=
r
sin
θ
,
x
2
=
y
; parabola
11.
(a)
r
cos
θ
= 7
(b)
r
= 3
(c)
r
2
−
6
r
sin
θ
= 0,
r
= 6 sin
θ
(d)
4(
r
cos
θ
)(
r
sin
θ
) = 9, 4
r
2
sin
θ
cos
θ
= 9,
r
2
sin 2
θ
= 9
/
2
12.
(a)
r
sin
θ
=
−
3
(b)
r
=
√
5
(c)
r
2
+ 4
r
cos
θ
= 0,
r
=
−
4 cos
θ
(d)
r
4
cos
2
θ
=
r
2
sin
2
θ
,
r
2
= tan
2
θ
,
r
= tan
θ