Find the locus of a point which moves so that the sum of the squares of its distances from the lines $x + y = 0$ and $x - y = 0$ is $4$.

Question

I have tried answering this question and my answer is $x^2+y^2=2$ yet the book says $x^2+y^2=4$. Help please.

Answer 1

Referring to the image below, it apparent that the locus you want is a circular arc, because for any angle $\alpha$, the sum of the squares $a^2+b^2=R^2$ and hence the circular arc must be $x^2+y^2=R^2=4$ or $R=2$.