The equation $2x^2 + 4xy - ky^2 + 4x + 2y - 1 = 0$ represents a pair of lines. The value of $k$ is

For what value of $p$ does the equation $y^2 + xy + px^2 - x - 2y = 0$ represent two straight lines?

The separate equations of the lines represented by the equation $3x^{2}-2\sqrt{3}xy-3y^{2}=0$ are

If in the general quadratic equation $f(x, y) = ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$,$\Delta = 0$ and $h^2 = ab$,then the equation represents:

If one of the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ is coincident with one of the lines represented by $a'x^2 + 2h'xy + b'y^2 = 0$,then:

The perpendiculars are drawn to lines $L_1$ and $L_2$ from the origin making an angle $\frac{\pi}{4}$ and $\frac{3 \pi}{4}$ respectively with the positive direction of the $X$-axis. If both the lines are at a unit distance from the origin,then their joint equation is