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An equation of a plane parallel to the plane $x-2 y+2 z-5=0$ and at a unit distance from the origin is
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$x-2 y+2 z-3=0$
$x-2 y+2 z-3=0$
Equation of plane parallel to $x-2 y+2 z-5=0$ is $x-2 y+2 z+k=0 \dots \dots(1)$
perpendicular distance from $\mathrm{O}(0,0,0)$ to $(1)$ is $1$
$\frac{|k|}{\sqrt{1+4+4}}=1 \quad \Rightarrow|k|=3 \quad \Rightarrow k=\pm 3 \quad \therefore x-2 y+2 z-3=0$
perpendicular distance from $\mathrm{O}(0,0,0)$ to $(1)$ is $1$
$\frac{|k|}{\sqrt{1+4+4}}=1 \quad \Rightarrow|k|=3 \quad \Rightarrow k=\pm 3 \quad \therefore x-2 y+2 z-3=0$
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