1 Answers to Chapter 7 Exercise 7A 1 a (13, 67.4°) b (13, 112.6°) c (13, 112.6°) d ( √ ___ 13, 56.3°) e (2, 30°) 2 a (3 √ __ 3, 3) b (3 √ __ 3, 3) c (3 √ __ 2, 3 √ __ 2) d (5 √ __ 2, 5 √ __ 2) e (2, 0) Exercise 7B 1 a x 2 y 2 4 b x 3 c y 5 2 a x 2 4ay or y x 2 ___ 4a b x 2 y 2 2ax or (x a) 2 y 2 a 2 c x 2 y 2 3ay or x 2 ( y 3a ___ 2 ) 2 9a 2 ___ 4 3 a (x 2 y 2 ) 3 _ 2 8y 2 b (x 2 y 2 ) 3 _ 2 2x 2 c x 2 1 or x 1 4 a r 4 b r 2 8 cosec 2c r 2 sin 25 a r 2 cos b r 2 4 _________ 1 sin 2c r 3 ___ √ __ 2 sec ( __ 4 ) 6 a arctan 2 b r a __ 2 cosec ( __ 3 ) c r tan sec a sec Exercise 7C 1 a Circle radius 6 6 b Half-line (half of y � x) 5π 4 c Half-line (half of y � �x) π 4 2 a 2 line x � 2 x y b 3 y � 3 x y c 4 x y 4 3 3 a Circle centre (0, ) radius x y a 2 a 2 a 2 b θ � 0 a 2a a c θ � 0 π 6 π 6 5π 6 3π 2 7π 6 π 2 θ � θ � � θ � Answers to Chapter 7
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1
Answers to Chapter 7
Exercise 7A 1 a (13, 67.4°) b (13, 112.6°) c (13, 112.6°) d ( √
___ 13 , 56.3°)
e (2, 30°) 2 a (3 √
__ 3 , 3) b (3 √
__ 3 , 3)
c (3 √__ 2 , 3 √
__ 2 ) d (5 √
__ 2 , 5 √
__ 2 )
e (2, 0)
Exercise 7B 1 a x2 y2 4 b x 3 c y 5
2 a x2 4ay or y x2 ___
4a
b x2 y2 2ax or (x a)2 y2 a2
c x2 y2 3ay or x2 ( y 3a ___ 2 ) 2 9a2
___ 4
3 a (x2 y2 ) 3 _ 2 8y2 b (x2 y2 )
3 _ 2 2x2
c x2 1 or x 1 4 a r 4 b r2 8 cosec 2
c r2 sin 2
5 a r 2 cos b r2 4 _________ 1 sin 2
c r 3 ___ √
__ 2 sec ( __
4 )
6 a arctan 2 b r a __ 2 cosec ( __
3 )
c r tan sec a sec
Exercise 7C 1 a
Circle radius 66
b
Half-line(half of y � x)
5π4
c
Half-line(half of y � �x)π
4
2 a
2
line x � 2
x
y
b
3 y � 3
x
y
c
4 x
y
4 3
3 a
Circle centre (0, ) radius
x
y
a2
a2
a2
b
θ � 0
a
2a
a
c
θ � 0
π6
π6
5π6
3π2
7π6
π2
θ �
θ � �
θ �
Answers to Chapter 7
2
ANSWERS
4 a
θ � 0
2a
3a
2a
a
b
θ � 0
6a
7a
6a
5a
c
θ � 0
4a
7aa
5 a
θ � 0
3a
2a 2a
a
b
θ � 0
7a
5a
6a 6a
c
θ � 0
7a
4c 4a
a
6 a
θ � 0
π
2π
2π
4π
b
θ � 0
a
c
θ � 0
Exercise 7D
1 a2 ____
8 2 3a2
_____ 4
3 ( 2)a2
_________ 48
4 a2 __
4
5 a2 ln √
__ 2 _______
2 or a
2 ln 2 ______ 4 6 2a23
_____ 3
7 a2 __
4 (11 24) 8
a2 (2p2 q2) ____________
2
9 a2 ____
12 10 a
2 __
4 [ __
4 3 √
__ 3 ____
16 ]
11 5 ___ 4
Exercise 7E
1 (2a, 0) and ( a __ 2 , 2 ___
3 ) , ( a __
2 , 2 _____
3 )
2 a (9.15, 1.11) b (212, 2.68)
3 a ( 2a ___ 3 , 0.421 ) b r a √
__ 6 ____
9 cosec
4 ( 7 1 _ 2 a, 1.32 ) 5 r cos 3 r cos 1 r 3 sec r sec