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The transformed equation of the curve $2 x^{2} + y^{2} - 3 x + 5 y - 8 = 0$ when the origin is translated to the point (-1, 2) is

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$2 X^{2} + Y^{2} - 7 X + 9 Y + 11 = 0$

$2 X^{2} + Y^{2} + 7 X + 9 Y + 11 = 0$

$2 X^{2} + Y^{2} + 7 X - 9 Y + 11 = 0$

$2 X^{2} + Y^{2} - X + Y + 11 = 0$

answer is A.

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Detailed Solution

Let $x = X - 1, y = Y + 2$
Transformed equation is
$2 {(X - 1)}^{2} + {(Y + 2)}^{2} - 3 (X - 1) + 5 (Y + 2) - 8 = 0$
$2 X^{2} + Y^{2} - 7 X + 9 Y + 11 = 0$

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