Question

If $a,b,c$ are in AP, then the straight line $ax+by+c=0$will always pass through the point

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

Answer 1

The correct option is B

$(1,-2)$

Explanation for the correct option:

Step 1. Find the points:

Given $a,b,c$ are in AP and straight line $ax+by+c=0...\left(i\right)$

So $2b=a+c$

$\Rightarrow$ $c=2b-a...\left(ii\right)$

Step 2. Substitute $\left(ii\right)$in$\left(i\right)$ we get

$ax+by+2b-a=0$

$\Rightarrow$$a(x-1)+b(y+2)=0$

$\Rightarrow$ $x-1=0$and $y+2=0$

$\Rightarrow$ $x=1,y=-2$

So, the equation satisfies at points $\mathbf{}\mathit{x}\mathbf{=}\mathbf{1}\mathbf{}\mathbf{,}\mathit{y}\mathbf{=}\mathbf{-}\mathbf{2}\mathbf{}$

Hence, Option ‘B’ is Correct.