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Question:

If the plane 2x-y+2z+3=0 has the distances 1/3 and 2/3 units from the planes 4x-2y+4z+λ=0 and 2x-y+2z+μ=0 respectively, then the maximum value of λ+μ is equal to:

5

13

15

9

Solution:

The correct option is C
4x-2y+4z+6=0
|λ-6|/√16+4+16 = 1/3
|λ-6|/6 = 1/3
|λ-6| = 2 ⇒ λ = 8, 4
|μ-3|/√4+4+1 = 2/3
|μ-3|/3 = 2/3
|μ-3| = 2 ⇒ μ = 5, 1
maximum value of (λ+μ) = 13