Question

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

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

Answer 1

The correct option is C $x+y=4$

On comparing $2a+2b+c=0$ with $ax+by+c=0,$ all the lines pass through $A(2,2)$
The line through $A(2,2)$ and farthest from $B(1,1)$ will be perpendicular to the line joining $A(2,2)$ and $B(1,1).$
Slope of line $AB$ is $m=\frac{2-1}{2-1}=1$
$\therefore$ Required equation of line passing through $A(2,2)$ is
$y-2=\frac{-1}{1}(x-2)$
$\Rightarrow x+y=4$