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Question
Mathematics
The equation of a circle which is co-axis with circles 2 x2+2 y2-2 x+6 y-3=0 x2+y2+4 x+2 y+1=0 It is given that the center of the circle to be determined lies on the radical axis of these two circles, is.
Q. The equation of a circle which is co-axis with circles
2
x
2
+
2
y
2
−
2
x
+
6
y
−
3
=
0&
x
2
+
y
2
+
4
x
+
2
y
+
1
=
0
It is given that the center of the circle to be determined lies on the radical axis of these two circles, is.
1943
200
Conic Sections
Report Error
A
4
x
2
+
4
y
2
+
6
x
−
10
y
−
1
=
0
B
4
x
2
+
4
y
2
+
6
x
+
10
y
+
1
=
0
C
4
x
2
+
4
y
2
+
6
x
+
10
y
−
1
=
0
D
None of these
Solution:
Radical axis :
S
1
−
S
2
=
0
and
S
1
+
λ
(
S
2
−
S
1
)
=
0
10
x
−
2
y
+
5
=
0
...(i)
and
(
x
2
+
y
2
+
4
x
+
2
y
+
1
)
+
λ
(
10
x
−
2
y
+
5
)
=
0
From (i),
−
20
−
50
λ
+
2
−
2
λ
+
5
=
0
⇒
λ
=
4
−
1
Required Circle:
(
x
2
+
y
2
+
4
x
+
2
y
+
1
)
−
4
1
(
10
x
−
2
y
+
5
)
=
0
⇒
4
x
2
+
4
y
2
+
16
x
+
8
y
+
4
−
10
x
+
2
y
−
5
=
0
⇒
4
x
2
+
4
y
2
+
6
x
+
10
y
−
1
=
0
