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Question

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 circumcentre of the triangle CAB (C being center of the circles) is

A
2x2+2y24x+1=0
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B
x2+y24x+2=0
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C
x2+y24x+1=0
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D
2x2+2y24x+3=0
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Solution

The correct option is D 2x2+2y24x+1=0
Let P be (1+2cosθ,2sinθ) and C is (1,0).
Circumcentre of triangle ABC is midpoint of PC.
2h=1+2cosθ+1
and 2k=2sinθ
[2(h1)]2+(2k)2=2
2(h1)2+k21=0
2x2+2y24x+1=0

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