Question

Locus of a point that is equidistant from the lines $x+y-2\sqrt{2}=0$ and $x+y-\sqrt{2}=0$ is

• A. $x+y-5\sqrt{2}=0$
• B. $x+y-3\sqrt{2}=0$
• C. $2x+2y-3\sqrt{2}=0$
• D. $2x+2y-5\sqrt{2}=0$

Answer 1

Answer: (C)

$2x+2y-3\sqrt{2}=0$

For any point $P(x,y)$ that is equidistant from given line, we have
$|x+y-\sqrt{2}|=|x+y-2\sqrt{2}|$
$x+y-\sqrt{2}=-(x+y-2\sqrt{2})$
$⟹2x+2y-3\sqrt{2}=0$
Hence, option 'C' is correct.