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 _____________.

Let point P(x, y) A(0, 0), B(1, 0), C(0, 1), D(1, 1) (PA)^(2) + (PB)^(2) + (PC)^(2) + (PD)^(2) = 18 x^2 + y^2 + x^2 + (y - 1)^2 + (x - 1)^2 + y^2 + \ (x - 1)^2 + (y - 1)^2 = 18 => 4(x^2 + y^2) - 4y - 4x = 14 => x^2 + y^2 - x - y - 7 / 2 = 0 d = 2sqrt 1 / 4 + 1 / 4 + 7 / 2 => d^2 = 16

The locus of a point which moves such that the sum of s... | null (Mathematics)

Let point P(x, y)
A(0, 0), B(1, 0), C(0, 1), D(1, 1)
(PA)² + (PB)² + (PC)² + (PD)² = 18

{x^2} + {y^2} + {x^2} + {(y - 1)^2} + {(x - 1)^2} + {y^2} + \\ {(x - 1)^2} + {(y - 1)^2} = 18

\Rightarrow 4({x^2} + {y^2}) - 4y - 4x = 14

\Rightarrow {x^2} + {y^2} - x - y - {7 \over 2} = 0

d = 2\sqrt {{1 \over 4} + {1 \over 4} + {7 \over 2}}

\Rightarrow {d^2} = 16

Explanation

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