The equation x^2 + 4xy + y^2 + 2x + 4y + 2 = | vedclass

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(C) The general equation of a second-degree curve is $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.Comparing this with the given equation $x^2 + 4xy + y^2

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$A$ hyperbola

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(C) The general equation of a second-degree curve is $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.Comparing this with the given equation $x^2 + 4xy + y^2 + 2x + 4y + 2 = 0$,we have $a = 1, h = 2, b = 1, g = 1, f = 2, c = 2$.First,we calculate the discriminant $h^2 - ab = (2)^2 - (1)(1) = 4 - 1 = 3$.Since $h^2 - ab > 0$,the conic section is a hyperbola.Next,we check the determinant $\Delta = abc + 2fgh - af^2 - bg^2 - ch^2 = (1)(1)(2) + 2(2)(1)(1) - (1)(2)^2 - (1)(1)^2 - (2)(2)^2 = 2 + 4 - 4 - 1 - 8 = -7$.Since $\Delta 
eq 0$ and $h^2 - ab > 0$,the equation represents a hyperbola.

The equation $x^2 + 4xy + y^2 + 2x + 4y + 2 = 0$ represents

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