If the quadrilateral formed by the lines ax+by+c=0 , a′x+b′y+c=0,ax+by+c′=0,a′x+b′y+c′=0 has  perpendicular diagonals, then

Since the diagonals are perpendicular, the given quadrilateral is a rhombus. So, the distances between two pairs of parallel sides are equal. Hence,c′−ca2+b2=∣c′−ca′2+b′2 or  a2+b2=a12+b12