Question

Assertion :One side of a rectangle lies along the line $4x+7y+5=0$. Two of its vertices are $(-3,1)$ and $(1,1)$. Equation of the side farthest from the origin is $7x-4y+25=0$ Reason: If $a$ and $b$ are constants $(a,b\ne 0)$ and $c$ is a variable, then from the lines $ax+by+c=0$ and $bx-ay-c=0$ the line farthest from the origin is the one for which $|c|$ is least.

• 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 C Assertion is correct but Reason is incorrect

Reason is false as the distance of any such line from origin is
$\left|\frac{\pm c}{\sqrt{a^2+b^2}}\right|$
which is maximum when $\left|c\right|$ is maximum.

Assertion
the other sides of the rectangle are $4x+7y=4+7=11,7x-4y=7-4=3$ and $7x-4y=-21-4=-25$
So the farthest from the origin is $7x-4y+25=0$