The pair of straight lines represented by the equation $\sqrt{3}x^2 - 4xy + \sqrt{3}y^2 = 0$ are

The angle between the lines represented by the equation $x^2 + 2xy \sec \theta + y^2 = 0$ is

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

$ax^2-4xy-2y^2=0$ 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 the lines represented by $(p - q) x^2 + 2 (p + q) xy + (q - p) y^2 = 0$ are perpendicular to each other,then:

The equation $x^2-3xy+\lambda y^2+3x-5y+2=0$,where $\lambda$ is a real number,represents a pair of lines. If $\theta$ is the acute angle between the lines,then $\frac{\operatorname{cosec}^2 \theta}{\sqrt{10}} = $