The equation of the lines passing through the origin and having slopes $3$ and $-\frac{1}{3}$ is

If two of the three lines represented by the equation $ax^3 + bx^2y + cxy^2 + dy^3 = 0$ are perpendicular,then:

If the equation $7x^2 - 14xy + py^2 - 12x + qy - 4 = 0$ represents a pair of parallel lines,then the value of $\sqrt{p^2 + q^2 - pq}$ is

If the slopes of the lines represented by the equation $6x^2 + 2hxy + 4y^2 = 0$ are in the ratio $2:3$,then the value of $h$ such that both the lines make acute angles with the positive $X$-axis measured in the positive direction is

The equation to the pair of straight lines through the origin which are perpendicular to the lines $2x^2 - 5xy + y^2 = 0$ is:

The combined equation of the lines passing through the origin making an acute angle $\alpha$ with the line $y=x$ is