Question

Assertion :If $a,b,c$ are in A. P. then straight line $ax+by+c=0$ will always passes through a fixed point $(1,-2)$. Reason: A straight line $ax+by+c=0$ will pass through a point $(x_1,y_1)$ if $a{x}_1+b{y}_1+c=0$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$a,b,c\in A.P.$

$\therefore 2b=a+c$

i.e. $a-2b+c=0$

Now $ax+by+c=0$ will pass through $(1,-2).$

if $a\left(1\right)+b(-2)+c=0\Rightarrow a-2b+c=0$ which is true.