The radius of the sphere $3 x^{2} + 3 y^{2} + 3 z^{2} - 8 x + 4 y + 8 z - 15 = 0$ is

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Solution

The correct option is A 3
Given that:
$3 x^{2} + 3 y^{2} + 3 z^{2} - 8 x + 4 y + 8 z - 15 = 0$
$⟹ x^{2} + y^{2} + z^{2} - \frac{8}{3} x + \frac{4}{3} y + \frac{8}{3} z - 5 = 0$
Compare it with equation of the sphere,
$x^{2} + y^{2} + z^{2} + 2 u x + 2 v y + 2 w z + d = 0$ , we get
$2 u = - \frac{8}{3}, 2 v = \frac{4}{3}, 2 w = \frac{8}{3}, d = - 5$
$⟹ u = - \frac{4}{3}, v = \frac{2}{3}, w = \frac{4}{3}, d = - 5$
Now, Radius of sphere $= \sqrt{u^{2} + v^{2} + w^{2} - d}$
$= \sqrt{\frac{16}{9} + \frac{4}{9} + \frac{16}{9} + 5} = \sqrt{4 + 5} = \sqrt{9} = 3$
Hence, B is the correct option.

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