Question

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

• 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 1

Answer: (A)

$x-2y+2z-3=0$

Let an equation of a plane parallel to the plane $x-2y+2z-5=0$ be $x-2y+2z+k=0$...(i)

Perpendicular distance from $O(0,0,0)$ to (1) is $1$

$\frac{|k|}{\sqrt{1+4+4}}=1$

$\Rightarrow |k|=3$

$\Rightarrow k=+3or-3$

$\therefore x-2y+2z-3=0$

Hence, option 'A' is correct.