Question

The equations of planes parallel to the plane x + 2y + 2z + 8 = 0, which are at a distance of 2 units from the point (1, 1, 2) are ________.

Options

• x + 2y + 2z - 5 = 0 or x + 2y + 2z - 3 = 0

• x + 2y + 2z - 6 = 0 or x + 2y + 2z - 7 = 0

• x + 2y + 2z - 13 = 0 or x + 2y + 2z - 1 = 0

• x + 2y + 2z + 3 = 0 or x + 2y + 2z - 5 = 0

Answer 1

The equations of planes parallel to the plane x + 2y + 2z + 8 = 0, which are at a distance of 2 units from the point (1, 1, 2) are x + 2y + 2z - 13 = 0 or x + 2y + 2z - 1 = 0.

Explanation:

Equation of plane parallel to the plane

x + 2y + 2z + 8 = 0 is x + 2y + 2z + λ = 0

Given distance from the point (1, 1, 2) to the plane.

x + 2y + 2z + λ = 0 is 2 units

∴ 2 = `|(1 + 2 + 4 + lambda)/(sqrt(1 + 4 + 4))|`

`=> +- 2 = (lambda + 7)/3`

⇒ λ + 7 ± 6 

∴ λ = - 13, - 1

Hence, equation of plane is

x + 2y + 2z - 13 = 0 or x + 2y + 2z - 1 = 0