Its intercepts on the x and y axes are a and b respectively.

It is given that

1/a + 1/b = constant = k (assume)

1/ka + 1/kb = 1

According to the given condition :

Hence 1/k, 1/k satisfies equation.

x/a + y/b = 1

Hence the line passes through the fixed point (1/k, 1/k)