Centre of the sphere $4 (x - 7) (x + 2) + 4 (y - 4) (y + 9) +$ $4 (z + 1) (z - 1) + 175 = 0$ is

(\frac{5}{2}, - \frac{5}{2}, 0)

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(\frac{- 5}{2}, - \frac{5}{2}, 0)

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(\frac{5}{2}, \frac{5}{2}, 0)

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(\frac{- 5}{2}, \frac{- 5}{2}, 0)

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Solution

The correct option is A $(\frac{5}{2}, - \frac{5}{2}, 0)$
Given, $4 (x - 7) (x + 2) + 4 (y - 4) (y + 9) +$ 4 $(z + 1) (z - 1) + 175 = 0$
$4 (x^{2} + y^{2} + z^{2}) - 20 x - 56 + 20 y - 144 - 4 + 175 = 0$
$x^{2} + y^{2} + z^{2} - 5 x + 5 y - 29 = 0$
Hence centre of the given sphere is $(\frac{5}{2}, \frac{- 5}{2}, 0)$

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