The values of for which equation x^2 - y^2 - x - y - 2 = 0 represents a pair of straight lines, are

JEE MainMathematicsEasyStraight Lines

The values of $\lambda$ for which equation x^2 - y^2 - x -
$\lambda$ y - 2 = 0 represents a pair of straight lines, are

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\left| \begin{matrix} 1 & 0 & - 1/2 \\ 0 & - 1 & - \lambda/2 \\ - 1/2 & - \lambda/2 & - 2 \end{matrix} \right| = 0 \Rightarrow \lambda = \pm 3

Source: Grass-G / M-11 Mathematics Paper-2 1Nov.docx

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