If $a, b, c$ are in A.P. then the straight line $a x+b y+c=0$ will always pass through a fixed point

Question

If $a, b, c$ are in A.P. then the straight line $a x+b y+c=0$ will always pass through a fixed point whose coordinates are .......

Professor PC Thomas Classes · Answer

Since $a, b, c$ are in A.P, $2 b=a+c$ Given equation of line is $$\begin{equation*}a x+b y+c=0 	ag{i} \end{equation*}$$ From (i) and (ii), we get $a x+b y+2 b-a=0$\ $\Rightarrow a(x-1)+b(y+2)=0$,\ which always passes through $(1,-2)$\