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x+y=1x+y=2x+y=2xy2x+2y=1

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ASolution :

The equation of line AB is y-1 = m(x-1). Therefore, the equation of line AC is <br> `y-1 = -(1)/(m)(x-1)` <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_CG_C02_E07_018_S01.png" width="80%"> <br> `2h=1-(1)/(m)` <br> `2k=1+(1)/(m)` <br> Eliminating m, we have locus x+y=1.