Question

Let $a,b,c$ are in A.P. then the line $ax+by+c=0$ always passes through which fixed point

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

Answer 1

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

Given, $a,b,c$ are in A.P. .

Then $b-a=c-b$

or, $c=2b-a$......(1).

Now the equation of the line $ax+by+c=0$ can be written as,

$ax+by+(2b-a)=0$ [ Using (1)]

or, $a(x-1)+b(y+2)=0$

This is true for all $a,b$ then $x-1=0$ and $y+2=0$ or, $x=1,y=-2$.

So the fixed point is $(1,-2)$.