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If the axes are shifted to (-2, -3) and rotated through $\frac{π}{4}$ then transformed equation of $2 x^{2} + 4 xy - 5 y^{2} + 20 x - 22 y - 14 = 0$ is

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$X^{2} - 14 X Y + 7 Y^{2} = 2$

$X^{2} + 14 X Y + 7 Y^{2} = 2$

$X^{2} - 14 X Y - 7 Y^{2} = 4$

$X^{2} - 14 X Y - 7 Y^{2} = 2$

answer is A.

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Detailed Solution

$(h, k) = (- 2, - 3), θ = 45^{0}$ using

$x - h = X \cos θ - Y \sin θ$

$y - k = X \sin θ + Y \cos θ$ subtute given equation

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