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  • Let P be any moving point on the circle. AB be the chord of c

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

Option: 1

\mathrm{2 x^2+2 y^2-4 x+1=0}


Option: 2

\mathrm{x^2+y^2-4 x+2=0}


Option: 3

\mathrm{x^2+y^2-14 x+1=0}


Option: 4

\mathrm{2 x^2+2 y^2-4 x+3=0}


Answers (1)

best_answer

\mathrm{\text { Let } P \text { be }(1+\sqrt{2} \cos \theta, \sqrt{2} \sin \theta) \text { and } C \text { is }(1,0) \text {. }}

Circum centre of triangle ABC lies on midpoint of PC

\mathrm{\begin{aligned} & \Rightarrow 2 h=1+\sqrt{2} \cos \theta+1 \text { and } 2 k=\sqrt{2} \sin \theta \\ & \Rightarrow[2(h-1)]^2+(2 k)^2=2 \\ & \Rightarrow 2(h-1)^2+k^2-1=0 \Rightarrow 2 x^2+2 y^2-4 x+1=0 \end{aligned}}

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vishal kumar

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