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

For $a, b, h > 0$,if the slope of one of the lines represented by $a^2 x^2 + 2hxy + b^2 y^2 = 0$ is twice that of the other,then the value of $\frac{h}{ab}$ is

The joint equation of the pair of lines passing through the origin with slopes $(1+\sqrt{2})$ and $\frac{1}{(1+\sqrt{2})}$ is

If $x^2+\alpha y^2+2 \beta y=a^2$ represents a pair of perpendicular lines,then $\beta$ equals to

If $ax^2-34xy-5y^2+2x+26y-5=0$ represents a pair of straight lines,then the value of $a$ is

If two lines represented by the equation $x^2 - (1 + \sqrt{3})xy + \sqrt{3}y^2 = 0$ make angles $\alpha$ and $\beta$ with the $X$-axis, then find the value of $\tan(\alpha + \beta)$.