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

The combined equation of the two diameters of a circle which divide the circle into $4$ sectors is $ax^2+2hxy+by^2=0$. If the area of the bigger sector is $5$ times the area of the smaller sector,then $\frac{|a+b|}{\sqrt{(a-b)^2+4h^2}} = $

If the lines represented by $(1+\sin^2 \theta) x^2+2hxy+2\sin \theta y^2=0$,where $\theta \in [0, 2\pi]$,are perpendicular to each other,then $\theta = \dots$.

If the lines represented by $(p - q) x^2 + 2 (p + q) xy + (q - p) y^2 = 0$ are perpendicular to each other,then:

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

For $\alpha \in [0, \frac{\pi}{2}]$,the angle between the lines represented by $[x \cos \theta - y][(\cos \theta + \tan \alpha) x - (1 - \cos \theta \tan \alpha) y] = 0$ is