Question

A point moves such that the sum of the square of its distance from the sides of a sqaure of side unity is equal to $9$. The locus of the point is a circle such that

• A. Center of the circle coincides with that of square
• B. Center of the circle is $(\frac{1}{2},\frac{1}{2})$
• C. Radius of the circle is $2$
• D. All the above are true

Answer 1

The correct option is D All the above are true

Let the sides of the square be $y=0,y=1,x=0$ and $x=1.$

Let the moving point be $(x,y).$

Then,$y^2+{(y-1)}^2+x^2+{(x-1)}^2=9$ is the equation of the locus.

$\Rightarrow 2x^2+2y^2-2x-2y-7=0,$

which represents a circle having centre $(\frac{1}{2},\frac{1}{2})$ (which is also the centre of the square) and radius $2.$