Concept:Standard Equation of a line y = mx + c, where m is the slope of the line.Slopes of parallel lines are equal. The parallel lines are equally inclined with the positive x-axis and hence the slope of parallel lines are equal. If the slopes of two parallel lines are represented as m1, m2 then we have m1 = m2.Calculation:Given:Lines ax + by + c = 0 and bx + ay + c = 0Express the two lines in standard format that is y = mx + cax + by + c = 0 ? by = -ax - c ? \(\displaystyle y=(\frac{-a}{b})x-\frac{c}{b}\) ------(i)bx + ay + c = 0 ? ay = -bx - c ? \(\displaystyle y=(\frac{-b}{a})x-\frac{c}{a}\) ------(ii)Given both lines are parallel implies their slopes are equal, that is? \(\displaystyle \frac{-a}{b}=\frac{-b}{a}\)? b2 = a2? a2 - b2 = 0? a2 - b2 = 0 is correct.