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

If one of the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ is $y = mx$,then

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

If the equation $ax^2 + 2hxy + by^2 = 0$ has one line as the bisector of the angle between the coordinate axes,then:

If the products of the perpendiculars from the origin to the pairs of lines $xy+x+y+1=0$,$x^2-y^2+2x+1=0$,and $2x^2+3xy-2y^2+2x+1=0$ are $p_1, p_2$,and $p_3$ respectively,then:

If the two lines given by $ax^2+2hxy+by^2=0$ make inclinations $\alpha$ and $\beta$ with the $x$-axis,then $\tan(\alpha+\beta)=$