Consider points A 
and B 
lying on x-axis. These points are rotated in an-anticlockwise direction about the origin through an angle of tan –1 
. Let the new position of A and B be A ′ and B ′ respectively. With A ′ as centre and radius 
a circle C 1 is drawn and with B ′ as a centre and radius 
circle C 2 is drawn. Find radical axis of C 1 and C 2 .
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
θ = tan –1 
⇒ tan θ = 
∴ sin θ = 
and cos θ = 
∴ A ′ ≡ (OA cos θ , OA sin θ ) ⇒ A ′ ≡ (3, 2)
Similarly B ′ ≡ (OB cos θ , OB sin θ ) ≡ (6, 4)
Now it can be checked that circles C 1 and C 2 touch each other.
Let the point of contact be C.
∴ C ≡ 
∴ required radical axis is a line perpendicular to
A ′ B ′ and passing through point C
y – 
= – 
(x – 5)
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