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

Options

A. `x-2y+2z-3=0`
B. `x-2y+2z+1=0`
C. `x-2y+2z-1=0`
D. `x-2y+2z+5=0`

Answer

A

Explanation

Equation of family of planes parallel to the givan plane is
`x-2y+2z+d=0`
Also, perpendicular distance from origin is 1 unit.
`:." "|{:(0-2(0)+2(0)+d)/(sqrt(1^(2)+2^(2)+2^(2))):}|=1`
`rArr" "|{:(d)/(3):}|=1rArrd=pm3`
Hence, the requation of the plane parallel to given plane and at unit distance from origin is
`x-2y+2zpm3=0`.