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

Let P=(x, y) be locus of point.

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

Now for a point (x, y) as per the given condition

$$\begin{gathered} \Rightarrow {\mathrm{x}}^2+{(1-\mathrm{y})}^2+{(1-\mathrm{x})}^2+{\mathrm{y}}^2=9 \\ \Rightarrow {\mathrm{x}}^2+{\mathrm{y}}^2+1-2\mathrm{y}+{\mathrm{x}}^2+1-2\mathrm{x}+{\mathrm{y}}^2=9 \\ \Rightarrow 2{\mathrm{x}}^2+2{\mathrm{y}}^2-2\mathrm{x}-2\mathrm{y}-7=0 \\ \Rightarrow {\mathrm{x}}^2+{\mathrm{y}}^2-\mathrm{x}-\mathrm{y}-\frac{7}{2}=0 \end{gathered}$$