The given lines are
a1x + b1y + c1 = 0 ... (1)
a1x + b1y + d1 = 0 ... (2)
a2x + b2y + c2 = 0 ... (3)
a2x + b2y + d2 = 0 ... (4)
The area of the parallelogram formed by the lines a1x + b1y + c1 = 0, a1x + b1y + d1 = 0, a2x + b2y + c2 = 0 and a2x + b2y + d2 = 0 is given below:
If the given parallelogram is a rhombus, then the distance between the pair of parallel lines are equal.