The lines represented by the equation $9x^2 + 24xy + 16y^2 + 21x + 28y + 6 = 0$ are

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:

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

If $\theta$ is the acute angle between the pair of lines $H \equiv ax^2 - xy + by^2 = 0$,$\tan \theta = 5$ and $(1, -1)$ is a point on $H = 0$,then $a^2 + ab + b^2 =$

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

The equation $3ax^2 - 16xy - (a^2 - 10)y^2 = 0$ represents