If the equation 12x^2 - 10xy + 2y^2 + 11x - 5 | vedclass

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(B) The general equation of the second degree $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of straight lines if $abc + 2fgh - af^2 - bg^

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$2$

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(B) The general equation of the second degree $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of straight lines if $abc + 2fgh - af^2 - bg^2 - ch^2 = 0$.Comparing the given equation $12x^2 - 10xy + 2y^2 + 11x - 5y + k = 0$ with the general form:$a = 12, b = 2, c = k, 2h = -10 \implies h = -5, 2g = 11 \implies g = 11/2, 2f = -5 \implies f = -5/2$.Substituting these values into the condition:$(12)(2)(k) + 2(-5/2)(11/2)(-5) - 12(-5/2)^2 - 2(11/2)^2 - k(-5)^2 = 0$$24k + 137.5 - 12(25/4) - 2(121/4) - 25k = 0$$24k - 25k + 137.5 - 75 - 60.5 = 0$$-k + 2 = 0 \implies k = 2$.

If the equation $12x^2 - 10xy + 2y^2 + 11x - 5y + k = 0$ represents two straight lines,then the value of $k$ is

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