TOPIC 29 | equation of circle set 1 of 7 get the full set details at the bottom of page
Question 1:
Find the radius and the equation of the circle whose center is (4, 3) and
passes through the origin.
Question 2:
0 has radius
Find the value of k for which the circle x 2 + y 2 − 4x − 2ky + 1 =
of 2 units
Question 3:
A circle passes through the point (4, 2) and it has the same centre as the
0 . Find the equation of the circle.
circle x 2 + y 2 − 4x + 4y − 2 =
Question 4:
A circle has a diameter AB where A is the point (6, 4) and B is the point
( −2,2) . Find
(a) the coordinates of the centre of the circle,
(b) the radius of the circle,
(c) the equation of the circle in general form.
Question 5:
(a) Find the centre and the length of radius of the circle
2x 2 + 2y 2 − 3x + 4y + 2 =
0
(b) Show that the line x − y + 3 =
0 will not intersect the circle
2
2
( x − 3) + ( y + 2) =
25 for all real values of x
Question 6:
A diameter of a circle has end points at A(2, –1) and B(4, 3). Find the
equation of the circle.
Question 7:
0 at two points, A
The line y + 7x =
34 cuts the circle x 2 + y 2 − 2x − 4y − 20 =
and B. Find
(i) the coordinates of A and B
(ii) the equation of the perpendicular bisector of AB
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TOPIC 29 | equation of circle set 1 of 7 get the full set details at the bottom of page
Question 8:
The diagram shows two point A( −3, − 6) and B(7 , − 6) on a circle with
centre G.
The equation of the tangent to the circle at the point Q(1, − 12) is
x + 5y + 59 =
0
(i) Show that the coordinates of G is ( 2, − 7 )
(ii) Find the equation of the circle.
Question 9:
The line x + 3y − 2 =
0 at two points A
0 cuts the circle x 2 + y 2 − 6x − 4y + 8 =
and B.
Find
(a) the mid-point of AB
(b) the equation of the perpendicular bisector of AB and hence show that it
passes through the centre of the circle
Question 10:
Find the centre and the radius of the circle x 2 + y 2 + 4x − 18y + 60 =
0
Question 11:
Given that PQ is a diameter of a circle such that P = ( –3, 0 ) and Q = ( 3,k )
and the length of PQ is 10 cm
(i) Find the value of k
(ii) Hence, find the equation of the circle
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TOPIC 29 | equation of circle set 1 of 7 get the full set details at the bottom of page
Question 12:
Find the coordinates of the centre C and radius of circle
x 2 + y 2 − 4x − 8y − 5 =
0
The line =
y 3x − 7 cuts the circle at points A and B.
(a) Find the coordinates of A and B.
(b) Calculate the area of the triangle ABC.
Question 13:
0
The equation of a circle, C, is x 2 + y 2 + 4x − 2y − 20 =
(i) Find the coordinates of the centre of C and find the radius of C
(ii) Show that the centre of C lies on the line =
y 7x + 15
(iii) Find the equation of the circle which is the reflection of C in the yaxis.
Question 14:
y
C(2, 3)
x
A
O
D
B
The diagram, not drawn to scale, shows a circle with centre C(2, 3) and
radius 5 units. The circle cuts the x-axis at A and B. The perpendicular
bisector of A and C cuts the x-axis at D. Find
(i) the equation of the circle,
(ii) the coordinates of A,
(iii) the midpoint of AC,
(iv) the gradient of AC,
(v) the coordinates of D.
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TOPIC 29 | equation of circle set 1 of 7 get the full set details at the bottom of page
Question 15:
State the equation of the circle if its centre is (–2, 0) and its diameter is 6
units.
Question 16:
0
The equation of a circle is given as x 2 + y 2 − 6x + 2y − 6 =
(a) State the coordinates of the centre of the circle.
(b) Find the radius of the circle.
(c) Find the value of k, where k > 0 , if A ( 3,k ) is a point on the circle.
(d) B ( –1,–1) is a point on the circle. Find the coordinates of C if BC is the
diameter of the circle
Question 17:
The equation of a circle, C, is x 2 + y 2 − 6x − 8y + 9 =
0
(i) Find the coordinates of the centre of the C and find the radius of C.
(ii) Show that C touches the x-axis.
r 2 , which
(iii) State the equation of the circle, in the form ( x − a)2 + ( y − b)2 =
is a reflection of C in the x-axis.
Question 18:
The equation of a circle, C is x 2 + y 2 − 8x + 2y − 17 =
0
(i) Find the coordinates of the centre of C and the radius of C.
(ii) Find the equation of a chord whose mid-point is (8 , − 2) .
Question 19:
Find the equation of the circle whose centre lies on the line y= 3 − x and
which passes through the point S(–3, –1) and T (1, 7).
Question 20:
Find the equation of the circle, where the x-axis and y-axis are tangents to
the circle, with radius 3 units.
The coordinates of the centre of the circle is (x, y) where x ≥ 0 and y ≥ 0 .
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