The locus of a point, which moves such that the sum of squares of its distances from the points ( 0 , 0 ) ,…

Let $P\left(x,y\right)$ be the required point. Then,

$x^2+y^2+(x-0{)}^2+(y-1{)}^2+(x-1{)}^2+(y-0{)}^2+(x-1{)}^2+(y-1{)}^2=18$

$\Rightarrow 4x^2+4y^2-4x-4y+4=18$

$\Rightarrow x^2+y^2-x-y-\frac{14}{4}=0$

Centre$\equiv \left(\frac{1}{2},\frac{1}{2}\right)$ and

Radius$,r=\sqrt{\frac{1}{4}+\frac{1}{4}+\frac{14}{4}}=2 \mathrm{units}$ 

So,

$d=2r=2\times 2=4$

$\Rightarrow d^2=16$