The locus of the points for which the sum of the squares of distances from the coordinate axes is $25$.
My solution- let $(x,y)$ be a point on the locus. Then distance from the coordinate axes will be $|x|$ and $|y|$. Then sum of squares is $x^2+y^2$ which is equal to $25$. Hence the answer is $x^2+y^2=25$. Is this the correct answer and approach. Please correct me if wrong and suggest a better approach.
The solution is correct.
Just to suggest another method, although I don't think it is better.
The sum of the squares of distances from the coordinate axes is equal to the square of the distance from the origin. So the point is 5 units away from the origin. The locus is the circle with centre at the origin and radius $5$.