For what value of k does the equation kx^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 $kx^2 - 10xy + 12y^2 + 5x - 16y - 3

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$2$

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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 $kx^2 - 10xy + 12y^2 + 5x - 16y - 3 = 0$,we get $a = k, h = -5, b = 12, g = 5/2, f = -8, c = -3$.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: $k(12)(-3) + 2(-8)(5/2)(-5) - k(-8)^2 - 12(5/2)^2 - (-3)(-5)^2 = 0$.$-36k + 200 - 64k - 75 + 75 = 0$.$-100k + 200 = 0$.$100k = 200$.$k = 2$.

For what value of $k$ does the equation $kx^2 - 10xy + 12y^2 + 5x - 16y - 3 = 0$ represent a pair of straight lines?

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