The locus of the point which moves in a plane so that the sum of the squares of its distances from the lines ax+by+c=0  and bx−ay+d=0  is r2, is a circle of radius.

The given lines are perpendicular.  So shifting the origin to their point of intersection if (h, k)  are the new coordinates of any point on the locus then h2+k2=r2 and the locus is x2+y2=r2  which is a circle of radius r.