Let A(1,4) and B(1,-5) be two points. Let P be a point on the circle (x-1)2+(y-1)2=1 such that (PA)2+(PB)2 have maximum value, then the points, P,A and B lie on:

P=(1+cosθ,1+sinθ),A=(1,4),B(1,-5)PA2+PB2=cos2θ+(sinθ-3)2+cos2θ+(sinθ+6)2=10-6sinθ+37+12sinθ=47+12sinθ-6sinθ=47+6sinθPA2+PB2max=(47+6sinθ)max⇒θ=π2 ∴p=(1,2)∴P,A,B lie on line x=1