If ab−cc+ba+cbc−aa−ba+bc=0, then the line ax + by + c = 0 passes through the fixed point which is

Applying C1→aC1 and then C1→C1+bC2+cC3, and taking a2+b2+c2 common from C1, we getΔ=a2+b2+c2a1b−cc+b1bc−a1b+ac=a2+b2+c2a1b−cc+b0c−a−b0a+c−b          R2→R2−R1,R3→R3−R1=a2+b2+c2a−bc+a2+ab+ac+bc     (expanding along C1)=a2+b2+c2(a+b+c)Hence, Δ=0⇒a+b+c=0Therefore, line ax + by + c = 0 passes through the fixed point (1, 1).