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

Practice worksheets for Core 1 topic cirles

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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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C1 CIRCLES Worksheet A continued
12 The circle C has the equation x2 + y2 - 4x - 4y - 28 = 0.
a Find the distance of the point A (10, 8) from the centre of C.
The tangent to C at the point B passes through A.
b Find the length AB.
13 A circle has the equation x2 + y2 + 6x - 2y = 0 and passes through the point P.…read more

Comments

daviesg

A good set of (basic) questions, finding the equation of circles given centre and radius.  Needs answers.

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