Which of the following equations does not rep | vedclass

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(C) general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of straight lines if the determinant $\Delta = \begin{vm

Vedclass · Accepted Answer

$y^2 - x + 1 = 0$

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(C) general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of straight lines if the determinant $\Delta = \begin{vmatrix} a & h & g \ h & b & f \ g & f & c \end{vmatrix} = 0$.For option $A$: $x^2 - x = 0 \implies x(x-1) = 0$,which represents lines $x=0$ and $x=1$.For option $B$: $xy - x = 0 \implies x(y-1) = 0$,which represents lines $x=0$ and $y=1$.For option $C$: $y^2 - x + 1 = 0$. This is a parabola,not a pair of lines,as it cannot be factored into two linear factors.For option $D$: $xy + x + y + 1 = 0 \implies x(y+1) + 1(y+1) = 0 \implies (x+1)(y+1) = 0$,which represents lines $x=-1$ and $y=-1$.Thus,the equation that does not represent a pair of lines is $y^2 - x + 1 = 0$.

Which of the following equations does not represent a pair of lines?

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