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Question Number 30166 by Tinkutara last updated on 17/Feb/18

Commented by ajfour last updated on 18/Feb/18

Commented by ajfour last updated on 18/Feb/18

centre of circle Q(1,1) point P of line (α,β) let centre of circumcircle of △APB be C(h,k). C is midpoint of QP. so 2h=α+1 , 2k=β+1 hence α = 2h−1 , β = 2k−1 As (α, β) lies on line lx+my+n=0 we have l(2h−1)+m(2k−1)+n=0 hence required locus is 2lx+2my+n = l+m .

centreofcircleQ(1,1)pointPofline(α,β)letcentreofcircumcircleof△APBbeC(h,k).CismidpointofQP.so2h=α+1,2k=β+1henceα=2h−1,β=2k−1As(α,β)liesonlinelx+my+n=0wehavel(2h−1)+m(2k−1)+n=0hencerequiredlocusis2lx+2my+n=l+m.

Commented by Tinkutara last updated on 18/Feb/18

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