Question

Equation(s) of the line perpendicular to $x=y$ and at a distance of $1$ unit from origin is/are

• A. $x+y+\sqrt{2}=0$
• B. $3x+4y+5=0$
• C. $x+y-\sqrt{2}=0$
• D. $3x+4y-5=0$

Answer 1

Answer: (A), (C)

The correct options are
A $x+y+\sqrt{2}=0$
C $x+y-\sqrt{2}=0$

Equation of the line perpendicular to $x=y$ will be of form $x+y+k=0$
Distance from origin to the required line is $1$ unit
$\frac{|k|}{\sqrt{2}}=1\Rightarrow k=\pm \sqrt{2}$
Hence required line equation's are
$x+y\pm \sqrt{2}=0$