**ANSWERS** - AS Maths - Core 1 - Solomon Answers - Circles - C

Answers to practice worksheets for Core 1 - topic cirles

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C1 CIRCLES Answers - Worksheet C
1 a (x - 4)2 - 16 + y2 + 7 = 0 2 a (x - 3)2 - 9 + (y + 1)2 - 1 - 15 = 0
centre (4, 0) centre (3, -1)
b (x - 4)2 + y2 = 9 b (x - 3)2 + (y + 1)2 = 25
radius = 3 radius = 5
2 - (-1) 3
c grad of radius = = 4
7-3
grad of tangent = - 4
3
y-2= -4
3
(x - 7)
3y - 6 = -4x + 28
4x + 3y - 34 = 0
3 a (x + 3)2 - 9 + (y - 4)2 - 16 + 21 = 0 4 a centre (0, 0) grad of radius = 1
(x + 3)2 + (y - 4)2 = 4 grad of tangent = -1
centre (-3, 4) radius 2 y - 5 = -(x - 5) [ y = 10 - x ]
b dist. of centre from O = 9 + 16 = 5 b grad of radius = -7
max. dist. of P from O grad of tangent = 17
=5+2=7 y+7= 1
7
(x - 1)
7y + 49 = x - 1
x - 7y - 50 = 0
c sub. x - 7(10 - x) - 50 = 0
x = 15
(15, -5)
5 a x2 + (y - a)2 - a2 = 0 6 a (x + 1)2 - 1 + (y - 7)2 - 49 + 30 = 0
x2 + (y - a)2 = a2 centre (-1, 7)
centre (0, a) radius a b (x + 1)2 + (y - 7)2 = 20
b C2: (x - b)2 - b2 + y2 = 0 radius = 20 = 2 5
(x - b)2 + y2 = b2, centre (b, 0) radius b c sub. y = 2x - 1 into eqn. of circle
y x2 + (2x - 1)2 + 2x - 14(2x - 1) + 30 = 0
x2 - 6x + 9 = 0
C1 (x - 3)2 = 0
a C2 repeated root tangent
point of contact (3, 5)
O b x
7 a (x - 3)2 - 9 + (y - 6)2 - 36 + 28 = 0 8 a radius = 16 + 4 = 20
centre (3, 6) (x - 8)2 + (y + 1)2 = 20
b sub. b sub. x = -2y - 4 into eqn. of circle:
x2 + (x - 2)2 - 6x - 12(x - 2) + 28 = 0 (-2y - 12)2 + (y + 1)2 = 20
x2 - 11x + 28 = 0 4y2 + 48y + 144 + y2 + 2y + 1 = 20
(x - 4)(x - 7) = 0 y2 + 10y + 25 = 0
x = 4, 7 (y + 5)2 = 0
A (4, 2), B (7, 5) repeated root tangent
AB = 9 + 9 = 18 = 3 2
Solomon Press

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C1 CIRCLES Answers - Worksheet C page 2
14 - 2
9 a grad = = 2
3
10 a (x - 1)2 - 1 + (y - 7 2
2
) - 49
4
- 16 = 0
8 + 10
y-2= 2
3
(x + 10) centre (1, 7
2
)
2 7 2
3y - 6 = 2x + 20 b (x - 1) + (y - 2
) = 117
4
9 ×13
2x - 3y + 26 = 0 radius…read more

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