Question

If $a,b,c$ are any three terms of an AP, then the line $ax+by+c=0$ _____________ .

• A. has a fixed direction
• B. always passes through a fixed point
• C. always cuts intercepts on the axes such that their sum is zero
• D. forms a triangle with the axes whose area is constant

Answer 1

The correct option is B always passes through a fixed point

As $a,b,c$ are in A.P
$a+c=2b\Rightarrow a-2b+c=0$
Hence, $ax+by+c=0$ always passes through $(1,-2).$