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 P A 2 + P B 2 have maximum value, then the points, P , A and B lie on

Step-by-step solution

P be a point on x - 1 2 + y - 1 2 = 1 , so P 1 + cos θ , 1 + sin θ . Given A 1 , 4   &   B 1 , - 5 P A 2 + P B 2 = cos θ 2 + sin θ - 3 2 + cos θ 2 + sin θ + 6 2 = 47 + 6 sin θ is maximum if sin θ = 1 ⇒ sin θ = 1 , cos θ = 0 P 1 , 2 ,   A 1 , 4 ,   B 1 , - 5 The points P ,   A and B lie on the line x = 1 .