Question

If a, b, c are in A.P., then the line ax + by + c = 0 passes through a fixed point. Write the coordinates of that point.

Answer 1

If, a, b, c are in A.P, then
a + c = 2b
⇒ a − 2b + c = 0
Comparing the coefficient of ax + by + c = 0 and a − 2b + c = 0, we get
x = 1 and y = −2
So, the the coordinates of that point is (1, −2)