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If the transformed equation of a curve is $3 X^{2} + X Y - Y^{2} - 7 X + Y + 7 = 0$ when the axes are translated to the point (1, 2), then the original equation of the curve is

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$3 x^{2} + x y - y^{2} + 15 x + 4 y + 13 = 0$

$3 x^{2} + x y - y^{2} - 15 x + 4 y + 13 = 0$

$3 x^{2} + x y + y^{2} - 15 x + 4 y + 13 = 0$

$3 x^{2} + x y - y^{2} + 15 x - 4 y + 13 = 0$

answer is B.

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Detailed Solution

X= x -1, Y = y-2

The original equation is $3 {(x - 1)}^{2} + {(x - 1)}^{2} + (x - 1) (y - 2) - {(y - 2)}^{2} - 7 (x - 1) + (y - 2) + 7 = 0$

$\Rightarrow 3 x^{2} + x y - y^{2} - 15 x + 4 y + 13 = 0$

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