Question

An equation of a plane parallel to the plane $x-2y+2z-5=0$ and at a unit distance from the origin is?

Answer 1

The correct answer is $x-2y+2z-3=0.$
Let an equation of a plane parallel to the plane $x−2y+2z−5=0$ be $x−2y+2z+k=0\ \ \ ...(i)$
Perpendicular distance from O(0,0,0) to (1) is 1
$\frac{|k|}{\sqrt{1+4+4}}=1$
$⇒|k|=3$
$⇒k=+3\ \ or−3$
$∴x−2y+2z−3=0$