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 d2 is equal to _____________.
Answer (integer)
16
Solution
Let point P(x, y)
<br><br>A(0, 0), B(1, 0), C(0, 1), D(1, 1)
<br><br>(PA)<sup>2</sup> + (PB)<sup>2</sup> + (PC)<sup>2</sup> + (PD)<sup>2</sup> = 18
<br><br>$${x^2} + {y^2} + {x^2} + {(y - 1)^2} + {(x - 1)^2} + {y^2} + {(x - 1)^2} + {(y - 1)^2}$$ = 18<br><br>$\Rightarrow 4({x^2} + {y^2}) - 4y - 4x = 14$<br><br>$\Rightarrow {x^2} + {y^2} - x - y - {7 \over 2} = 0$<br><br>$d = 2\sqrt {{1 \over 4} + {1 \over 4} + {7 \over 2}}$<br><br>$\Rightarrow {d^2} = 16$
About this question
Subject: Mathematics · Chapter: Circles · Topic: Equation of a Circle
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