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

Question

Philoid · Accepted Answer

Since the planes are parallel to x + 2y – 2z + 8 = 0, they must be of the form:

x + 2y – 2z + θ = 0

We know, the distance of point (x₁,y₁,z₁) from the plane

is given by:

According to the question, the distance of the planes from (2, 1, 1) is 2 units.

⟹

⟹ or

⟹ θ = 4 or –8

⟹ The required planes are:

x + 2y – 2z + 4 = 0 and x + 2y – 2z – 8 = 0