The lines $ax^2+2hxy+by^2=0$ are at right angles if

If the pair of lines $2x^2 + 3xy + y^2 = 0$ makes angles $\theta_1$ and $\theta_2$ with the positive direction of the $X$-axis,then $|\tan(\theta_1 - \theta_2)| = $

The angle between the lines represented by $ax^2 + 2hxy + by^2 = 0$ is:

Find the angle between the lines represented by $2x^2 - 7xy + 3y^2 = 0$ in degrees. (in $^o$)

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 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: