Circles Part 1

P be a point on circle
(x−1)2+(y−1)2=1
So, coordinate of P will be of form P(1+cos‌θ,1+sin‌θ)
Given, points A(1,4) and B(1,−5)
Then,
‌(PA)2+(PB)2
‌‌=cos2θ+(sin‌θ−3)2+cos2θ+(sin‌θ+6)2
‌‌=2cos2θ+2sin2θ−6‌sin‌θ+12‌sin‌θ+45
‌‌=47+6‌sin‌θ
Now,
(PA)2+(PB)2=47+6‌sin‌θ‌ is ‌
Maximum, when sin‌θ=1
θ‌θ‌=π∕2
⇒‌cos‌θ‌=0
‌P(1,2),A(1,4),B(1,−5)
∴P,A,B are collinear points on the line x=1