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

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 angle between the pair of straight lines $x^2 - y^2 - 2y - 1 = 0$ is....$^o$

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:

$ax^2-4xy-2y^2=0$ represents a pair of lines. If $\theta$ is the angle between these lines,$\cos \theta=\frac{1}{5}$ and the possible values of '$a$' are $a_1$ and $a_2$ $(a_1 < a_2)$,then $a_1+3a_2=$

If $\theta_1$ and $\theta_2$ are the acute angles between the pairs of lines $3x^2 - 7xy + 4y^2 = 0$ and $6x^2 - 5xy + y^2 = 0$ respectively,then: