If the circles x2+y2+2cx+b=0 and x2+y2+cx+b=0 touch each other, then
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Answer:
represents the circle with centre C
1
≡(−a,−b) & radius r
1
=
a
2
+b
2
−c
S
2
:x
2
+y
2
+2bx+2ay+c=0⇒ represents the circle with centre C
2
≡(−b,−a) & radius r
2
=
a
2
+b
2
−c
Distance between centre =
(a−b)
2
+(a−b)
2
=
2
(a−b)
case - 1
2
(a−b)=r
1
+r
2
=2
a
2
+b
2
−c
( touching externally )
2a
2
+2b
2
−4ab=4a
2
+4b
2
−4c
2a
2
+2b
2
+4ab=4c
(a+b)
2
=2c
case - 2
2
(a−b)=r
1
−r
2
=0 ( Touching internally ) which is not possible.
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