In order to eliminate the first degree terms in the equation $4 x^{2} - 4 y^{2} + z^{2} - 8 x + 16 y + 4 z - 25 = 0$ , the origin should be shifted to the point

(1, 2, - 2)

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(1, 2, - 1)

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(- 1, 2, 1)

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(1, - 2, 1)

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Solution

The correct option is A $(1, 2, - 2)$
The equation can be write as $4 (x - 1)^{2} - 4 (y - 2)^{2} + (z + 2)^{2} - 17 = 0$ .
So in order to avoid first degree term origin should shift to $(1, 2, - 2)$ .

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