If the equation 2x^2 + 7xy + 3y^2 - 9x - 7y + | vedclass

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(A) For the general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ to represent a pair of lines,the condition is $abc + 2fgh - af^2 -

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$4$

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(A) For the general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ to represent a pair of lines,the condition is $abc + 2fgh - af^2 - bg^2 - ch^2 = 0$.Comparing the given equation $2x^2 + 7xy + 3y^2 - 9x - 7y + k = 0$ with the standard form:$a = 2, b = 3, c = k, h = 7/2, g = -9/2, f = -7/2$.Substituting these values into the condition:$(2)(3)(k) + 2(-7/2)(-9/2)(7/2) - 2(-7/2)^2 - 3(-9/2)^2 - k(7/2)^2 = 0$.$6k + 441/4 - 49/2 - 243/4 - 49k/4 = 0$.Multiplying the entire equation by $4$ to clear the denominators:$24k + 441 - 98 - 243 - 49k = 0$.$-25k + 100 = 0$.$25k = 100$.$k = 4$.

If the equation $2x^2 + 7xy + 3y^2 - 9x - 7y + k = 0$ represents a pair of lines,then $k$ is equal to

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