Comprehension

निर्देश: निम्नलिखित प्रश्नों के लिए निम्नलिखित को ध्यान में रखें:

माना 2x2 + 2y2 + 2z2 + 3x + 3y + 3z - 6 = 0 एक गोला है।

गोले का केंद्र किस समतल पर स्थित है?

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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Detailed Solution

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व्याख्या:

गोले का केंद्र C \((\frac{-3}{4}, \frac{-3}{4}, \frac{-3}{4})\) है

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

समतल गोले के केंद्र को संतुष्ट करता है - 3 -6 - 6 + 15 = 0

⇒ 0 = 0

∴ विकल्प (d) सही है

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