The equation of a sphere with centre $(- 1, 2, - 3)$ and of radius $3$ is

x^{2} + y^{2} + z^{2} - 2 x + 4 y - 6 z + 5 = 0

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x^{2} + y^{2} + z^{2} + 2 x - 4 y + 6 z + 5 = 0

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x^{2} + y^{2} + z^{2} - 2 x - 4 y + 6 z - 5 = 0

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x^{2} + y^{2} + z^{2} + 2 x + 4 y + 6 z + 5 = 0

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Solution

The correct option is B $x^{2} + y^{2} + z^{2} + 2 x - 4 y + 6 z + 5 = 0$
Equation of sphere with centre $(- 1, 2, - 3)$ and radius $3$ is given by
$(x + 1)^{2} + (y - 2)^{2} + (z + 3)^{2} = 3^{2}$
$\Rightarrow x^{2} + y^{2} + z^{2} + 2 x - 4 y + 6 z + 5 = 0$

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