If the equation ax^2 + by^2 + cx + cy = 0 rep | 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 condi

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$c(a + b) = 0$

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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 $ax^2 + by^2 + cx + cy = 0$ with the general equation,we have:$A = a, B = b, C = 0, H = 0, G = c/2, F = c/2$.Substituting these values into the condition:$a(b)(0) + 2(c/2)(c/2)(0) - a(c/2)^2 - b(c/2)^2 - 0(0)^2 = 0$.This simplifies to:$-a(c^2/4) - b(c^2/4) = 0$.Multiplying by $-4$,we get:$ac^2 + bc^2 = 0$.$c^2(a + b) = 0$.Therefore,$c(a + b) = 0$.

If the equation $ax^2 + by^2 + cx + cy = 0$ represents a pair of straight lines,then

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