The equation of the sphere whose centre is $(1, - 1, 1)$ and whose radius is same as that of the sphere $2 x^{2} + 2 y^{2} + 2 z^{2} - 2 x + 4 y + 6 z - 1 = 0$

x^{2} + y^{2} + z^{2} + 2 x + 2 y + 2 z + 1 = 0

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x^{2} + y^{2} + z^{2} + 2 x + 2 y - 2 z - 1 = 0

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x^{2} + y^{2} + z^{2} - 2 x + 2 y - 2 z - 1 = 0

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x^{2} + y^{2} + z^{2} - 2 x - 2 y - 2 z - 1 = 0

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Solution

The correct option is D $x^{2} + y^{2} + z^{2} - 2 x + 2 y - 2 z - 1 = 0$
Radius of given sphere is $= \sqrt{{(\frac{1}{2})}^{2} + 1^{2} + {(\frac{3}{2})}^{2} + \frac{1}{2}} = 2$
Hence equation of required sphere with centre $(1, - 1, 1)$ is given by,
$(x - 1)^{2} + (y + 1)^{2} + (z - 1)^{2} = 2^{2}$
$\Rightarrow x^{2} + y^{2} + z^{2} - 2 x + 2 y - 2 z - 1 = 0$

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