# **ANSWERS** - AS Maths - Core 1 - Solomon Answers - Circles - A

Answers to practice worksheets for Core 1 - topic cirles

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C1 CIRCLES Answers - Worksheet A
1 a x2 + y2 = 25 b (x - 1)2 + (y - 3)2 = 4 c (x - 4)2 + (y + 6)2 = 1
d (x + 1)2 + (y + 8)2 = 9 e (x + 1 2
2
) + (y - 1 2
2
) = 1
4
f (x + 3)2 + (y - 9)2 = 12
2 a centre (0, 0) radius 4 b centre (6, 1) radius 9 c centre (-1, 4) radius 11
d centre (7, 0) radius 0.3 e centre (-2, -5) radius 4 2 f centre (8, -9) radius 6 3
3 a x2 + (y - 2)2 - 4 + 3 = 0 b (x - 1)2 - 1 + (y - 5)2 - 25 - 23 = 0
x2 + (y - 2)2 = 1 (x - 1)2 + (y - 5)2 = 49
c (x + 6)2 - 36 + (y - 4)2 - 16 + 36 = 0 d (x - 1)2 - 1 + (y + 8)2 - 64 = 35
(x + 6)2 + (y - 4)2 = 16 (x - 1)2 + (y + 8)2 = 100
e (x - 4)2 - 16 + (y + 3)2 - 9 = 0 f (x + 5)2 - 25 + (y - 1)2 - 1 - 19 = 0
(x - 4)2 + (y + 3)2 = 25 (x + 5)2 + (y - 1)2 = 45
g x2 + y2 - x - 6y + 1
4
=0 h x2 + y2 + 2
3
x- 8
3
y+ 8
9
=0
1 2 2 1 2 4 2
(x - 2
) - 1
4
+ (y - 3) - 9 + 1
4
=0 (x + 3
) - 1
9
+ (y - 3
) - 16
9
+ 8
9
=0
1 2 2 1 2 4 2
(x - 2
) + (y - 3) = 9 (x + 3
) + (y - 3
) =1
centre ( 1
2
, 3) radius 3 centre ( - 1
3
, 4
3
4 a radius = 9 + 16 = 5 (x - 1)2 + (y + 2)2 = 25
b radius = 25 + 4 = 29 (x + 5)2 + (y - 7)2 = 29
5 a centre ( 1+
2
3
, -2) = (2, -2) b centre ( -72+1 , 2 +
2
8
) = (-3, 5) c centre ( 1+
2
4
, 1+ 0
2
)=(5
2
, 1
2
)
4
+1
4
= 5
2
(x - 2)2 + (y + 2)2 = 1 (x + 3)2 + (y - 5)2 = 25 (x - 5 2
2
) + (y - 1 2
2
) = 5
2
10 - 1 9 - 10
6 a grad PQ = = 3, grad QR = = -1
3
3-0 6-3
3
) = -1
PQ and QR are perpendicular
PQR is a right-angle
b PQR is a right-angle PR is a diameter of C
centre is ( 0 +
2
6 1+ 9
, 2 ) = (3, 5)
(x - 3)2 + (y - 5)2 = 25
x2 - 6x + 9 + y2 - 10y + 25 - 25 = 0
x2 + y2 - 6x - 10y + 9 = 0
Solomon Press

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### Page 2

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C1 CIRCLES Answers - Worksheet A page 2
7 a centre (0, 0) radius 8 b (x - 1)2 - 1 + (y - 3)2 - 9 - 26 = 0
dist. pt to centre = 9 (x - 1)2 + (y - 3)2 = 36
outside circle centre (1, 3) radius 6

### Page 3

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C1 CIRCLES Answers - Worksheet A page 3
14 a (x - 3)2 - 9 + (y - 5)2 - 25 + 16 = 0 15 a (x + 2)2 - 4 + y2 = 13
centre (3, 5) centre (-2, 0)
5-2 0-4
3-6 -2 + 1
c y - 2 = -(x - 6) [y=8-x] y - 4 = 4(x + 1) [ y = 4x + 8 ]
b (x + 1)2 - 1…read more

### Page 4

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C1 CIRCLES Answers - Worksheet A page 4