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Let P be any moving point on the circle $x^{2} + y^{2} - 2 x = 1$ AB be the chord of contact of this point w.r.t. the circle $x^{2} + y^{2} - 2 x = 0$ The locus of the circumcenter of triangle CAB (C being the center of the circle) is

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2x2+2y2−4x+1=0

x2+y2−4x+2=0

x2+y2−4x+1=0

2x2+2y2−4x+3=0

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detailed solution

Correct option is A

Let P be (1+2cos⁡θ,2sin⁡θ) and C be (1,0)The circumcenter of triangle ABC is the midpoint of PC.Therefore,2h=1+2cos⁡θ+1 and 2k=2sin⁡θor [2(h−1)]2+(2k)2=2or 2(h−1)2+k2−1=0or 2x2+2y2−4x+1=0

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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 circumcenter of triangle CAB (C being the center of the circle) is

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Let P be any moving point on the circle $x^{2} + y^{2} - 2 x = 1$ AB be the chord of contact of this point w.r.t. the circle $x^{2} + y^{2} - 2 x = 0$ The locus of the circumcenter of triangle CAB (C being the center of the circle) is