Find the equations of het planes parallel to the plane `x+2y-2z+8=0` which are at distance of 2 units from the point `(2,1,1)dot`

Explanation

Let equation of plane parallel to plane `x+2y-2z+18=0`
`x+2y-2z+lambda = 0 "….."(1)`
Perpendicular distance from `(2,1,1)` to this plane
`|(2+2-2+lambda)/(sqrt(1+4+4))|=|(lambda+2)/(3)|`
Given that `|(lambda+2)/(3)| = 3 rArr (lambda+2)/(3) = +-3`
`rArr lambda+2=+-9`
`rArr lambda = 7` or ` lambda = - 11`
From eq. (1)
Required equations of planes
`x+2y-2z+7=0`
or `x+2y-2z-11 = 0`.