Find the equations of the planes parallel to the plane x+2y+2z+8=0 which are at the distance of 2 units from the point (1, 1, 2).
We know that
Equation of planes parallel to given plane x+2y+2z+8=0 is
x+2y+2x+λ=0....(1)
where λ− is a variable
Now this plane is at 2 unit
distance from point P(1,1,2)
D=∣∣
∣
∣∣ax1+by1+cz1+d√a21+b21+c21∣∣
∣
∣∣
2=∣∣
∣∣1(1)+2(1)+2(2)+λ√(1)2+(2)2+(2)2∣∣
∣∣
2=∣∣∣7+λ√9∣∣∣
Hence
λ=(−7±6)=−13,−1
So equation of required plane is
x+2y+2z−13=0−−−(A)
x+2y+2z−1=0−−−−(B)