If the equation Ax^2 + 2Bxy + Cy^2 + Dx + Ey | vedclass

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(D) The general second-degree equation $Ax^2 + 2Bxy + Cy^2 + Dx + Ey + F = 0$ represents a pair of straight lines if and only if the determinant of th

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None of these

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(D) The general second-degree equation $Ax^2 + 2Bxy + Cy^2 + Dx + Ey + F = 0$ represents a pair of straight lines if and only if the determinant of the matrix $\begin{bmatrix} A & B & D/2 \ B & C & E/2 \ D/2 & E/2 & F \end{bmatrix}$ is equal to $0$.This condition is given by $ACF + 2B(D/2)(E/2) - A(E/2)^2 - C(D/2)^2 - F(B^2) = 0$.This condition does not uniquely determine the sign of $B^2 - AC$. For a pair of straight lines,$B^2 - AC$ can be positive (intersecting lines),zero (parallel lines),or negative (imaginary lines). Therefore,none of the given options are universally correct.

If the equation $Ax^2 + 2Bxy + Cy^2 + Dx + Ey + F = 0$ represents a pair of straight lines,then the condition for $B^2 - AC$ is:

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