The equation $x^2 + ky^2 + 4xy = 0$ represents two coincident lines,if $k =$

The joint equation of the pair of lines passing through the origin and making an angle of $\frac{\pi}{4}$ with the line $3x + y - 6 = 0$ is

If the equation $3x^{2}+10xy+3y^{2}+16y+k=0$ represents a pair of lines,then the value of $k$ 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 joint equation of two lines passing through the origin and perpendicular to the lines given by $2 x^2+5 x y+3 y^2=0$ is

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