If the equation $3x^{2}+10xy+3y^{2}+16y+k=0$ represents a pair of lines,then the value of $k$ is

If the slopes of the lines represented by $Kx^2 - 4xy + 5y^2 = 0$ differ by $2$,then $K = $

If the lines represented by the equation $6x^2 + 41xy - 7y^2 = 0$ make angles $\alpha$ and $\beta$ with the $x$-axis,then $\tan \alpha \cdot \tan \beta = $

The separate equations of the lines represented by $4x^{2}-y^{2}+2x+y=0$ are

The joint equation of the pair of lines passing through $(2,3)$ and parallel to the lines represented by $x^{2}-y^{2}=0$ is:

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