The equation to the sphere concentric with the sphere $x^{2} + y^{2} + z^{2} - 2 x + 3 y - 8_{Z} - 1 = 0$ and passing through the point $(- 1, 2, 0)$ is

x^{2} + y^{2} + z^{2} - 2 x + 3 y - 8 z - 13 = 0

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x^{2} + y^{2} + z^{2} - 2 x + 3 y - 8 z - 9 = 0

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x^{2} + y^{2} + z^{2} - 2 x + 3 y - 8 z + 6 = 0

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x^{2} + y^{2} + z^{2} - 2 x + 3 y - 8 z + 4 = 0

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Solution

The correct option is A $x^{2} + y^{2} + z^{2} - 2 x + 3 y - 8 z - 13 = 0$
Equation of sphere concentric to given sphere is given by,
$x^{2} + y^{2} + z^{2} - 2 x + 3 y - 8_{Z} + k = 0$
Now it also passes through $(- 1, 2, 0)$
$\Rightarrow 1 + 4 + 0 + 2 + 6 + 0 = 0 \Rightarrow k = - 13$
Hence, required sphere is,
$x^{2} + y^{2} + z^{2} - 2 x + 3 y - 8_{Z} - 13 = 0$

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B (- 1, 0, - 2)

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