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Form 3 Equations of a Circle Topical Questions and Video Answers
The equation of a circle centre (a,b) is
x
2
+
y
2
-
6
x
-
10
y
+
30
=
0
. Find the values of a and b.
(5m 19s)
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1.
Obtain the centre and radius of the circle represented by the equation
X
2
+
y
2
-
10
y
+
16
=
0
2.
The equation of a circle is given by
x
2
+
4
x
+
y
2
-
5
=
0
. Find the radius and the centre of the circle.
3.
The points with coordinates (5,5) and (-3,-1) are the ends of a diameter of a circle centre A. Determine: (a) The coordinates of A (b) The equation of the circle, expressing it in form
x
2
+
y
2
+
a
x
+
b
y
+
c
=
0
where a, b and c are constant.
4.
Find the radius and the coordinates of the centre of the circle whose equation is
2
x
2
+
2
y
2
-
3
x
+
2
y
+
1
2
=
0
5.
The equation of a circle is given by
4
x
2
+
4
y
2
-
8
x
+
20
y
-
7
=
0
. Determine the coordinates of the centre of the circle.
6.
A circle whose equation is
(
x
-
1
)
2
+
(
y
-
k
)
2
=
10
passes through the point (2,5). Find the coordinates of the two possible centres of the circle.
7.
The circle shown on the next page cuts the x-axis at (-2,0) and (4,0). It also cuts y-axis (0,2) and (0,-4). Determine the: (a) (i) coordinates of the centre (ii)radius of the circle (b) Equation of the circle in the form x2+y2+ax+by=c where a, b, and c are constants.
8.
The equation of a circle centre (a,b) is
x
2
+
y
2
-
6
x
-
10
y
+
30
=
0
. Find the values of a and b.
9.
The equation of a circle is given by
x
2
+
4
x
+
y
2
-
2
y
-
4
=
0
. Determine the centre and radius of the circle.
10.
The diameter of a circle, centre O has its end points M (-1, 6) and N (5,-2). Find the equation of the circle in form
x
2
+
y
2
+
a
x
+
b
y
=
c
where a, b, and c are constants.
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