If the equation kxy + 10x + 8y + 16 = 0 repre | vedclass

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(C) The general equation of a second-degree curve is $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$. For this to represent a pair of straight lines,the cond

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$k = 0$ or $k = 5$

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(C) The general equation of a second-degree curve is $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$. For this to represent a pair of straight lines,the condition is $abc + 2fgh - af^2 - bg^2 - ch^2 = 0$. Comparing the given equation $kxy + 10x + 8y + 16 = 0$ with the general form,we have: $a = 0, b = 0, c = 16, h = k/2, g = 5, f = 4$. Substituting these values into the condition: $(0)(0)(16) + 2(4)(5)(k/2) - (0)(4^2) - (0)(5^2) - (16)(k/2)^2 = 0$. $0 + 20k - 0 - 0 - 16(k^2/4) = 0$. $20k - 4k^2 = 0$. $4k(5 - k) = 0$. Thus,$k = 0$ or $k = 5$.

If the equation $kxy + 10x + 8y + 16 = 0$ represents a pair of lines,then

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