If `a ,\ b , c` are in A.P., then the line `a x+b y+c=0` passes through a fixed point. write the coordinates of that point.

Explanation

Because a,b,c are in AP,

therefore` 2b=a+c`.

Putting the value of b in
`ax+by+c=0`, we get

`ax+(a+c)/2​y+c=0`

or, `a(2x+y)+c(y+2)=0`

or, `(2x+y)+[c/a​](y+2)=0`

This equation represents a family of straight lines passing through the intersection of
2x+y=0 and y+2=0, i.e. (1,−2).