# AS Maths - Core 1 - Solomon Worksheets - Circles - Worksheet A

Practice worksheets for Core 1 topic cirles

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- Created by: Charlotte Wilding
- Created on: 17-05-12 08:55

First 450 words of the document:

C1 CIRCLES Worksheet A

1 Write down an equation of the circle with the given centre and radius in each case.

a centre (0, 0) radius 5 b centre (1, 3) radius 2 c centre (4, -6) radius 1

d centre (-1, -8) radius 3 e centre ( - 1

2

, 1

2

) radius 1

2

f centre (-3, 9) radius 2 3

2 Write down the coordinates of the centre and the radius of each of the following circles.

a x2 + y2 = 16 b (x - 6)2 + (y - 1)2 = 81 c (x + 1)2 + (y - 4)2 = 121

d (x - 7)2 + y2 = 0.09 e (x + 2)2 + (y + 5)2 = 32 f (x - 8)2 + (y + 9)2 = 108

3 Find the coordinates of the centre and the radius of each of the following circles.

a x2 + y2 - 4y + 3 = 0 b x2 + y2 - 2x - 10y - 23 = 0

c x2 + y2 + 12x - 8y + 36 = 0 d x2 + y2 - 2x + 16y = 35

e x2 + y2 = 8x - 6y f x2 + y2 + 10x - 2y - 19 = 0

g 4x2 + 4y2 - 4x - 24y + 1 = 0 h 9x2 + 9y2 + 6x - 24y + 8 = 0

4 Find an equation of the circle

a with centre (1, -2) which passes through the point (4, 2),

b with centre (-5, 7) which passes through the point (0, 5).

5 Find an equation of the circle in which AB is a diameter in each case.

a A (1, -2) B (3, -2) b A (-7, 2) B (1, 8) c A (1, 1) B (4, 0)

6 The points P (0, 1), Q (3, 10) and R (6, 9) all lie on circle C.

a Show that PQR is a right-angle.

b Hence, show that C has the equation x2 + y2 - 6x - 10y + 9 = 0.

7 Find in each case whether the given point lies inside, outside or on the given circle.

a (0, -9) x2 + y2 = 64 b (4, 7) x2 + y2 - 2x - 6y - 26 = 0

c (7, -3) x2 + y2 + 10x - 4y = 140 d (-4, 1) x2 + y2 + 2x + 8y - 13 = 0

8 The point P lies on the circle with equation x2 + y2 + 12x - 6y + 27 = 0 and the point Q has

coordinates (8, 1). Find the minimum length of PQ giving your answer in the form k 2 .

9 Find an equation of the circle which crosses the x-axis at the points (2, 0) and (8, 0) and touches

the y-axis at the point (0, 4).

10 Given that the circle with equation x2 + y2 + 8x - 12y + k = 0 does not touch or cross either of

the coordinate axes, find the set of possible values of the constant k.

11 The circle C passes through the points P, Q and R with coordinates (-2, -2), (2, -4) and (7, 1)

respectively.

a Find an equation of the perpendicular bisector of the points P and Q.

b Find the coordinates of the centre of C.

c Find an equation of C.

Solomon Press

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