The locus of a point, which moves such that the sum of squares of its distances from the points ( 0 , 0 ) , ( 1 , 0 ) , ( 0 , 1 ) ( 1 , 1 ) is 18 units, is a circle of diameter d . Then d 2 is equal to

Step-by-step solution

Let P x , y be the required point. Then, x 2 + y 2 + ( x − 0 ) 2 + ( y − 1 ) 2 + ( x − 1 ) 2 + ( y − 0 ) 2 + ( x − 1 ) 2 + ( y − 1 ) 2 = 18 ⇒ 4 x 2 + 4 y 2 − 4 x − 4 y + 4 = 18 ⇒ x 2 + y 2 − x − y − 14 4 = 0 Centre ≡ 1 2 , 1 2 and Radius , r = 1 4 + 1 4 + 14 4 = 2   units So, d = 2 r = 2 × 2 = 4 ⇒ d 2 = 16