The lines represented by the equation $x^2-y^2-x+3y-2=0$ are :

If the sum and product of the slopes of the lines represented by $4x^2 + 2hxy - 7y^2 = 0$ are equal,then $h = \dots$

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 joint equation of the pair of lines passing through the point $(3, -2)$ and perpendicular to the lines $5x^2 + 2xy - 3y^2 = 0$ is:

The joint equation of the pair of lines passing through $(3, -2)$ and parallel to the lines represented by $x^{2} - 4xy + 3y^{2} = 0$ is:

If the slope of one line of the pair of lines represented by $ax^2 + 4xy + y^2 = 0$ is $3$ times the slope of the other line,then $a$ is