A new origin is chosen so that the equation $2 x^{2} + 7 y^{2} + 8 x - 14 y + 15 = 0$ may be translated to the form in which the first-degree terms be missing. Then the transformed equation is

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$2 X^{2} + 7 Y^{2} = 0$

$2 X^{2} + 7 Y^{2} = 9$

$2 X^{2} + 71 Y^{2} = 0$

$2 X^{2} - 7 Y^{2} = 0$

answer is A.

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Detailed Solution

Compare with ${ax}^{2} + 2 hxy + {by}^{2} + 2 gx + 2 fy + c = 0$
R.P = $(\frac{- g}{a}, \frac{- f}{b})$
The T.E is $2 {(X - 2)}^{2} + 7 {(Y + 1)}^{2} + 8 (X - 2) - 14 (Y + 1) + 15 = 0$

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