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NDA 2 2024 Maths, question 66

Topic: Analytical geometry

Passage · Q65 to Q66

Let 2x2+2y2+2z2+3x+3y+3z−6=02x^{2}+2y^{2}+2z^{2}+3x+3y+3z-6=0 be a sphere.

Q66

The centre of the sphere lies on the plane

  1. (a) 2x+2y+2z−3=02x+2y+2z-3=0
  2. (b) 4x+4y+4z−3=04x+4y+4z-3=0
  3. (c) 4x+8y+8z−15=04x+8y+8z-15=0
  4. (d) 4x+8y+8z+15=04x+8y+8z+15=0Correct answer

Solution.

Answer: (d) 4x+8y+8z+15=04x+8y+8z+15=0

  1. Completing squares gives the centre (−3/4,−3/4,−3/4).
  2. Substitution into (d) gives 4(−3/4)+8(−3/4)+8(−3/4)+15=−3−6−6+15=0.
  3. None of the other plane equations vanishes there.