Question

If a point moves such that the sum of the squares of its distance from the four sides of a unit square having $2$ sides along coordinate axis is $2$ , then the locus of the point is

• A. $x^2+y^2-x-y=0$
• B. $x^2+y^2+x+y=0$
• C. $x^2+y^2-2x-2y=0$
• D. $x^2+y^2=2$

Answer 1

The correct option is A $x^2+y^2-x-y=0$

Let $(h,k)$ is the point and equation of sides of square are : $x=0,x=1,y=0$ and $y=1$,
then sum of square of its distances from sides is $h^2+(1-h{)}^2+k^2+(1-k{)}^2$
Given : $h^2+(1-h{)}^2+k^2+(1-k{)}^2=2$
$\Rightarrow 2h^2+2k^2-2h-2k=0$
$\Rightarrow h^2+k^2-h-k=0$
$\therefore$locus: $x^2+y^2-x-y=0$