If the equation hxy + gx + fy + c = 0 represe | vedclass

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

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$fg = ch$

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(B) The general equation of a second-degree curve is $ax^2 + by^2 + 2hxy + 2gx + 2fy + c = 0$. 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 $hxy + gx + fy + c = 0$ with the general form,we have $a = 0, b = 0, h' = h/2, g = g/2, f = f/2, c = c$. Substituting these values into the condition: $0(0)(c) + 2(f/2)(g/2)(h/2) - 0(f/2)^2 - 0(g/2)^2 - c(h/2)^2 = 0$. This simplifies to $\frac{fgh}{4} - \frac{ch^2}{4} = 0$. Multiplying by $4$,we get $fgh - ch^2 = 0$,which implies $h(fg - ch) = 0$. Since $h 
eq 0$ for the $xy$ term to exist,we must have $fg = ch$.

If the equation $hxy + gx + fy + c = 0$ represents a pair of straight lines,then

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