Which of the following second-degree equation | vedclass

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Question

(C) general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of straight lines if the determinant $\Delta = abc + 2fg

Vedclass · Accepted Answer

$4x^2 - 4xy + y^2 = 4$

Vedclass · Answer

(C) general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of straight lines if the determinant $\Delta = abc + 2fgh - af^2 - bg^2 - ch^2 = 0$.For option $(c)$,the equation is $4x^2 - 4xy + y^2 - 4 = 0$.Here,$a = 4, h = -2, b = 1, g = 0, f = 0, c = -4$.Calculating the determinant: $\Delta = (4)(1)(-4) + 2(0)(-2)(0) - 4(0)^2 - 1(0)^2 - (-4)(-2)^2 = -16 + 0 - 0 - 0 + 16 = 0$.Since $\Delta = 0$,the equation $4x^2 - 4xy + y^2 = 4$ represents a pair of straight lines (specifically,parallel lines $(2x - y)^2 = 4$ or $2x - y = \pm 2$).

Which of the following second-degree equations represents a pair of straight lines?

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