If a , b and c are in A. P. then 2b = a + c or b =
a+c
2
Also the given line is ax + by + c = 0 Substituting the value of b we get ax + (
a+c
2
)y + c = 0 i.e., 2ax + (a + c) y + 2c = 0 for all values of a and c the (1 , - 2) satisfy the equation so the lines passes through a fixed point (1 , -2)