The equation 2y^2 - xy - x^2 + 6x - 8 = 0 rep | vedclass

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(A) The general second-degree equation is $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.Comparing this with $2y^2 - xy - x^2 + 6x - 8 = 0$,we have $a = -1,

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$A$ pair of straight lines

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(A) The general second-degree equation is $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.Comparing this with $2y^2 - xy - x^2 + 6x - 8 = 0$,we have $a = -1, h = -1/2, b = 2, g = 3, f = 0, c = -8$.The condition for the equation to represent a pair of straight lines is $\Delta = abc + 2fgh - af^2 - bg^2 - ch^2 = 0$.Substituting the values: $\Delta = (-1)(2)(-8) + 2(0)(3)(-1/2) - (-1)(0)^2 - (2)(3)^2 - (-8)(-1/2)^2$.$\Delta = 16 + 0 - 0 - 18 - (-8)(1/4) = 16 - 18 + 2 = 0$.Since $\Delta = 0$,the equation represents a pair of straight lines.

The equation $2y^2 - xy - x^2 + 6x - 8 = 0$ represents

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