The joint equation of the pair of lines passing through the origin and making an angle of $\frac{\pi}{6}$ with the line $3x+y-6=0$ is

Which of the following second-degree equations represents a pair of straight lines?

The joint equation of two lines passing through $(-2, 3)$ and parallel to the bisectors of the angle between the co-ordinate axes is

Assertion $(A)$: The difference of the slopes of the lines represented by $y^2 - 2xy \sec^2 \alpha + (3 + \tan^2 \alpha)(\tan^2 \alpha - 1) x^2 = 0$ is $4$.
Reason $(R)$: The difference of the slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ is $\frac{2 \sqrt{h^2 - ab}}{|b|}$.

The combined equation of a possible pair of adjacent sides of a square with area $16 \text{ square units}$ whose centre is the point of intersection of the lines $x+2y-3=0$ and $2x-y-1=0$ is

The product of the perpendiculars drawn from the origin to the lines represented by the equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ is: