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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2024 · Mathematics · Three Dimensional Geometry

Paragraph: Let 2 x^2+2 y^2+2 z^2+3 x+3 y+3 z-6=0 be a sphere....

Paragraph: Let 2x2+2y2+2z2+3x+3y+3z−6=02 x^2+2 y^2+2 z^2+3 x+3 y+3 z-6=0 be a sphere.
Question: The centre of the sphere lies on the plane

Options

  1. A2x+2y+2z−3=02 x+2 y+2 z-3=0
  2. B4x+4y+4z−3=04 x+4 y+4 z-3=0
  3. C4x+8y+8z−15=04 x+8 y+8 z-15=0
  4. D4x+8y+8z+15=04 x+8 y+8 z+15=0

Correct answer

D. 4x+8y+8z+15=04 x+8 y+8 z+15=0

Step-by-step solution

Centre of sphere is C(−34,−34,−34)4x+8y+8z+15=0\mathrm{C}\left(\frac{-3}{4}, \frac{-3}{4}, \frac{-3}{4}\right)^{4} x+8 y+8 z+15=0 is the only plane which satisfy the centre of sphere −3+−6−6+15=0⇒0=0-3+-6-6+15=0 \Rightarrow 0=0 Option (d) is correct.
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