The transformed equation of 2x2−3y2+z2+4x+6y−4z−2=0 when the axes are translated to the point −1,1,2 is

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The transformed equation of $2 x^{2} - 3 y^{2} + z^{2} + 4 x + 6 y - 4 z - 2 = 0$ when the axes are translated to the point $(- 1, 1, 2)$ is

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$2 x^{2} - 3 y^{2} + z^{2} = 10$

$2 x^{2} - 3 y^{2} + z^{2} = 5$

$2 x^{2} - 3 y^{2} + z^{2} = 15$

$2 x^{2} + 3 y^{2} + z^{2} = 5$

answer is B.

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Detailed Solution

$x = X - 1 y = Y + 1 Z = z + 2$
Required equation is $2 x^{2} - 3 y^{2} + z^{2} = 5$

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