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JEE Main2012MathematicsThree Dimensional GeometryActual

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

Options

  1. Ax-2 y+2 z-3=0
  2. Bx-2 y+2 z+1=0
  3. Cx-2 y+2 z-1=0
  4. Dx-2 y+2 z+5=0

Correct answer

A. x-2 y+2 z-3=0

Step-by-step solution

Equation of plane parallel to x-2 y+2 z-5=0 is x-2 y+2 z+k=0 (1) perpendicular distance from O (0,0,0) to (1) is 1 |k| 1+4+4 =1 |k|=3 k= 3 x-2 y+2 z-3=0

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