Let P be any moving point on the circle x2+y2−2x=1. AB be the chord of contact of this point w.r.t. the circle x2+y2−2x=0. The locus of the circumcentre of the triangle CAB (C being center of the circles) is
A
2x2+2y2−4x+1=0
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B
x2+y2−4x+2=0
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C
x2+y2−4x+1=0
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D
2x2+2y2−4x+3=0
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Solution
The correct option is D2x2+2y2−4x+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(h−1)]2+(2k)2=2 ⇒2(h−1)2+k2−1=0 ⇒2x2+2y2−4x+1=0