What is the equation of the sphere concentric with the sphere x^{2}+y^{2}+z^{2}-2x-6y-8z-5=0 and which passes through the origin?
- A. x^{2}+y^{2}+z^{2}-2x-8z=0
- B. x^{2}+y^{2}+z^{2}-2x-6y=0
- C. x^{2}+y^{2}+z^{2}-6y-8z=0
- D. x^{2}+y^{2}+z^{2}-2x-6y-8z=0 ✓
Correct Answer: D. x^{2}+y^{2}+z^{2}-2x-6y-8z=0
Explanation
A sphere concentric to another sphere has the same x, y, z coefficients, differing only in the constant term. Its equation is x^2+y^2+z^2-2x-6y-8z+k=0. Since it passes through the origin (0,0,0), substituting these coordinates gives k=0. The equation is therefore x^2+y^2+z^2-2x-6y-8z=0.
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