The point at which the line segment joining A 1,1 and B 5,5 subtends an obtuse angle is

Step-by-step solution

Equation of the circle assuming A B as the diameter is x - 1 x - 5 + y - 1 y - 5 = 0 ⇒ x 2 + y 2 - 6 x - 6 y + 10 = 0 Now, for point P h , k and circle S = 0 , if S 1 < 0 , then the point h , k lies inside the circle S = 0 and at this point diameter of the circle subtends an obtuse angle. Now, from options, we get, 7 - 1 7 - 5 + 7 - 1 7 - 5 > 0 0 - 1 0 - 5 + 5 - 1 5 - 5 > 0 2 - 1 2 - 5 + 4 - 1 4 - 5 < 0 1 - 1 1 - 5 + 5 - 1 5 - 0 = 0 Hence, 2,4 is the required point