The lines represented by the equation $9x^2 + 24xy + 16y^2 + 21x + 28y + 6 = 0$ are

The pair of lines $l x^2 + 2(l+m) x y + m y^2 = 0$ lies along two diameters of a circle and divides the circle into $4$ sectors. If the area of the bigger sector is $5$ times the area of the smaller sector,then $\frac{l m}{(l+m)^2} = $

The angle between the lines represented by the equation $x^{2}-xy-6y^{2}-7x+31y-18=0$ is

If the lines represented by $(k^2+2) x^2+3 xy-6 y^2=0$ are perpendicular to each other,then the values of $k$ are

The angle between the lines represented by $(\sin ^2 \alpha) y^2 - 2xy(\cos ^2 \alpha) + (\cos ^2 \alpha - 1) x^2 = 0$ is

If the angle between the two lines represented by $2x^2 + 5xy + 3y^2 + 6x + 7y + 4 = 0$ is $\tan^{-1} m$,then $m = $