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  • 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 <img alt="\mathrm{d^2}" src

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 \mathrm{d^2}  is equal to

Option: 1

16


Option: 2

10


Option: 3

-16


Option: 4

12


Answers (1)

best_answer

Let P(x, y) be any point, according to the question, we have
\mathrm{ (x-0)^2+(y-0)^2+(x-1)^2+(y-0)^2+(x-0)^2 \\ }

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

\mathrm{ \Rightarrow 4 x^2+4 y^2-4 x-4 y+4=18 \\ }

\mathrm{ \Rightarrow x^2+y^2-x-y=\frac{7}{2} \\ }
\mathrm{ \Rightarrow\left(x-\frac{1}{2}\right)^2+\left(y-\frac{1}{2}\right)^2=4 }

which is equation of circle with radius, \mathrm{ r=2 \Rightarrow }  Diameter, d=4
\mathrm{ \therefore \quad d^2=16 }

Posted by

himanshu.meshram

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