Comprehension

Direction: Consider the following for the items that follow:

Let 2x2 + 2y2 + 2z2 + 3x + 3y + 3z - 6 = 0 be a sphere.

The centre of the sphere lies on the plane 

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 2x + 2y + 2z - 3 = 0
  2. 4x + 4y + 4z - 3 = 0
  3. 4x + 8y + 8z - 15 = 0
  4. 4x + 8y + 8z + 15 = 0

Answer (Detailed Solution Below)

Option 4 : 4x + 8y + 8z + 15 = 0
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NDA 01/2025: English Subject Test
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Detailed Solution

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Explanation:

The Centre of the sphere is C \((\frac{-3}{4}, \frac{-3}{4}, \frac{-3}{4})\)

4x + 8y + 8z + 15 = 0,

Plane satisfy the centre of sphere – 3 –6 – 6 + 15 = 0 

⇒ 0 = 0

∴ Option (d) is correct

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