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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2023 · Mathematics · Three Dimensional Geometry

What is the equation of the sphere concentric with the sphere...

What is the equation of the sphere concentric with the sphere x2+y2+z2−2x−6y−8z−5=0x^2+y^2+z^2-2 x-6 y-8 z-5=0 and which passes through the origin?

Options

  1. Ax2+y2+z2−2x−8z=0x^2+y^2+z^2-2 x-8 z=0
  2. Bx2+y2+z2−2x−6y=0x^2+y^2+z^2-2 x-6 y=0
  3. Cx2+y2+z2−6y−8z=0x^2+y^2+z^2-6 y-8 z=0
  4. Dx2+y2+z2−2x−6y−8z=0x^2+y^2+z^2-2 x-6 y-8 z=0

Correct answer

D. x2+y2+z2−2x−6y−8z=0x^2+y^2+z^2-2 x-6 y-8 z=0

Step-by-step solution

Since, equation of sphere concentric with the sphere x2+y2+z2−2x−6y−8z−5=0x^2+y^2+z^2-2 x-6 y-8 z-5=0 is x2+y2+z2−2x−6y−8z+k=0x^2+y^2+z^2-2 x-6 y-8 z+k=0 Since, (0,0,0)(0,0,0) satisfy ⇒k=0\Rightarrow k=0 So, x2+y2+z2−2x−6y−8z=0x^2+y^2+z^2-2 x-6 y-8 z=0
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