A equation of a plane parallel to the plane $$x-2y+2z-5=0$$ and at a unit distance from the origin is :
JEE · Math · previous-year question
- A.$$x-2y+2z-3=0$$correct
- B.$$x-2y+2z+1=0$$
- C.$$x-2y+2z-1=0$$
- D.$$x-2y+2z+5=0$$
Answer
A. $$x-2y+2z-3=0$$
Explanation
Given equation of a plane is $$x - 2y + 2z - 5 = 0$$ So, Equation of parallel plane is given by $$x - 2y + 2z + d = 0$$ Now, it is given that distance from origin to the parallel planes is $$1.$$ $$\therefore$$ $$\left| {{d \over {\sqrt {{1^2} + {2^2} + {2^3}} }}} \right| = 1 \Rightarrow d = \pm 3$$ So equation of required plane $$x - 2y + 2z \pm 3 = 0$$
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