Question

Let $2a+2b+c=0$ , then the equation of the straight line $ax+by+c=0$ which is farthest from the point $\left(1,1\right)$ is

• A. $y=x$
• B. $y+x=2$
• C. $y+x=4$
• D. $y=x+2$

Answer 1

Answer: (C)

All the lines $ax+by+c=0$ pass through the point $\left(2,2\right).$
The line passing through $\left(2,2\right)$ & farthest from $\left(1,1\right)$ is perpendicular to the line joining $\left(1,1\right)$ &$\left(2,2\right)$
Now, the slope of the line joining $\left(1,1\right)$ &$\left(2,2\right)$ is $\frac{2-1}{2-1}=1$
$\Rightarrow$ The slope of the required line is $-1$
$\Rightarrow$ Required line is $\frac{y-2}{x-2}=-1$
$\Rightarrow y+x=4$