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Find the transformed form of the equation 2x^2 + 4xy + 3y^2 = 0 if the origin is shifted to the point (1, 1)

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Find the transformed form of the equation 2x2 + 4xy  + 3y2 = 0 if the origin is shifted to the point (1, 1)

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Put x = X + 1, y = Y + 1 in the given equation.

We get

2(X + 1)2 + 4(X + 1)(X + 1)(Y + 1) + 3 (Y + 1)2 = 0

⇒ 2X2 + 4xy + 3Y2 + 8X + 10Y + 9 = 0

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