Consider points 
and 
lying on 
-axis. These points are rotated in ananticlockwise direction about the origin through an angle of 
. Let the new position of 
and 
be 
and 
respectively. With 
as centre and radius 
a circle 
is drawn and with 
as a centre and radius 
circle 
is drawn. Find radical axis of 
and 
.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
9x + 6y = 65
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 
and 
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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