Question

If a point moves so that the sum of the squares of its distance from the four sides of a square is constant, then this point always lies on

• A. a straightline
• B. a circle
• C. a parabola
• D. an ellipse

Answer 1

The correct option is B a circle

Let four sides of a square as, $x=0,x=a,y=0,y=a$
And let $P(h,k)$ be the moving point.
Thus according to the given condition,
$\left(k^2\right)+(a-k{)}^2+(h^2)+(a-h{)}^2=\text{constant}=2c\text{(say)}$
$\Rightarrow h^2+k^2-ah-ak=c$
Thus locus of $P(h,k)$ is $x^2+y^2-ax-ak=c$, which is clearly a circle.
Hence option $B$ is correct choice.