The angle between the pair of lines $x^{2}+2xy-y^{2}=0$ is

The angle between the lines $ab(x^2 - y^2) + (a^2 - b^2)xy = 0$ is

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

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

The angle between the lines represented by the equation $x^2 + 2xy \sec \theta + y^2 = 0$ is

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} = $