The angle between the lines $x^2 + 4xy + y^2 = 0$ is ..... $^o$.

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} = $

If the pair of lines given by $(x^2+y^2) \cos^2 \theta = (x \cos \theta + y \sin \theta)^2$ are perpendicular to each other,then $\theta$ is equal to

The acute angle between the lines $(x^2+y^2) \sin \theta+2xy=0$ is

The angle between the lines $xy = 0$ is ............. $^\circ$.

If the coordinate axes are the bisectors of the angles between the pair of lines $ax^2 + 2hxy + by^2 = 0$,where $h^2 > ab$ and $a \neq b$,then