Equation of planes parallel to the plane x-2 y+2 z+4=0 which are at a distance of one unit from the point (1,2,3) are

Step-by-step solution

The equation of planes parallel to the plane x-2 y+2 z+4=0 is x -2 y +2 z + =0 The required planes are at a distance of one unit from (1,2,3) aligned & | ax ₁+ by ₁+ cz z₁+ d a ^2+ b ^2+ c ^2 |=1 & | 1(1)+(-2)(2)+2(3)+ 1+4+4 |=1 | 1-4+6+ 3 |=1 3+ = 3 & 3+ =3 or 3+ =-3 & =0 or =-6 aligned The equation of planes are x-2 y+2 z=0 and x-2 y+2 z-6=0