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Let P be any moving point on the circle x2+y22x=1 AB be the chord of contact of this point w.r.t. the circle x2+y22x=0 The locus of the circumcenter of triangle CAB (C being the center of the circle) is

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a
2x2+2y24x+1=0
b
x2+y24x+2=0
c
x2+y24x+1=0
d
2x2+2y24x+3=0

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detailed solution

Correct option is A

Let P be (1+2cosθ,2sinθ) and C be (1,0)
The circumcenter of triangle ABC is the midpoint of PC.
Therefore,
2h=1+2cosθ+1 and 2k=2sinθ
or [2(h1)]2+(2k)2=2
or 2(h1)2+k21=0
or 2x2+2y24x+1=0

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