Question

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

• A. $(1,-2)$
• B. $(-1,2)$
• C. $(1,2)$
• D. $(-1,-2)$

Answer 1

The correct option is A $(1,-2)$

Given that $a,b$ and $c$ are in AP
$\therefore$ $2b=a+c$
$\Rightarrow$ $c=2b-a$
and equation of straight line is
$ax+2by+c=0$
$\Rightarrow$ $ax+2b+(2b-a)=0$
$\Rightarrow$ $a(x-1)+b(2y+2)=a.0+b.0$
On comparing, we get
$x-1=0\Rightarrow x=1$
and $2y+2=0$
$\Rightarrow$ $y=-1$
Hence, the required fixed point is $(1,-1)$