Question

If line $y-x+2=0$ is shifted parallel to itself towards the x-axis by a perpendicular distance of $3\sqrt{2}$ units, then the equation of the new line may be

• A. $y=x+4$
• B. $y=x+1$
• C. $y=x-(2+3\sqrt{2})$
• D. $y=x-8$

Answer 1

Answer: (A), (D)

The correct options are
A $y=x+4$
D $y=x-8$

Let the new line be $y-x+c=0$
Then distance between the two parallel lines will be
$=\frac{|c-2|}{\sqrt{2}}$
$=3\sqrt{2}$
Hence
$|c-2|=6$
$c=8$ and $c=-4$
Hence the equations of the parallel lines will be
$y-x+8=0$ and $y-x-4=0$
Or
$y=x-8$ and $y=x+4$.