2016/086) If a,b,c are in AP find the fixed point wthough which line $ax+by+c= 0$ passes

a,b,c are in AP so $a+c = 2b$ or $c = 2b-a$
$ax+by+c=0$
$=>ax + by + (2b-a)=0$ or $(x-1) a + (y+2) b=0$
so the point through which the lines pass is (1,-2) as the above equation should be independent of (a,b)