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 angle between the pair of lines given by the equation $ax^2+4xy+2y^2=0$ is $45^{\circ}$,then the possible values of $a$ are:

If $\theta$ is the angle between the lines $x^2+2 h x y+b y^2=0$,then the angle between $x^2+2 x y \sec \theta+y^2=0$ is

If the angle between the pair of straight lines represented by the equation ${x^2} - 3xy + \lambda {y^2} + 3x - 5y + 2 = 0$ is ${\tan ^{ - 1}}\left( {\frac{1}{3}} \right)$,where $\lambda$ is a non-negative real number,then $\lambda$ is:

The angle between the lines represented by $x^2 - y^2 - 2y - 1 = 0$ is .....$^o$

The acute angle between the lines $6x^2 + 11xy - 10y^2 = 0$ is