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NDA2023MathematicsThree Dimensional GeometryActual

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

Options

  1. Ax^2+y^2+z^2-2 x-8 z=0
  2. Bx^2+y^2+z^2-2 x-6 y=0
  3. Cx^2+y^2+z^2-6 y-8 z=0
  4. Dx^2+y^2+z^2-2 x-6 y-8 z=0

Correct answer

D. x^2+y^2+z^2-2 x-6 y-8 z=0

Step-by-step solution

Since, equation of sphere concentric with the sphere x^2+y^2+z^2-2 x-6 y-8 z-5=0 is x^2+y^2+z^2-2 x-6 y-8 z+k=0 Since, (0,0,0) satisfy k=0 So, x^2+y^2+z^2-2 x-6 y-8 z=0

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