One of the lines represented by the equation ${x^2} + 6xy = 0$ is

If the equation $3x^2 + xy - y^2 - 3x + 6y + k = 0$ represents a pair of lines,then $k$ is equal to

If $m_{1}$ and $m_{2}$ are slopes of the lines represented by $(\sec^{2} \theta - \sin^{2} \theta) x^{2} - 2 \tan \theta xy + \sin^{2} \theta y^{2} = 0$,then $|m_{1} - m_{2}| = $

If the equation $2x^2 + 7xy + 3y^2 - 9x - 7y + k = 0$ represents a pair of lines,then $k$ is equal to

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

If the equation $x^2 + y^2 + 2gx + 2fy + 1 = 0$ represents a pair of straight lines,then: