The equations of the lines represented by the equation ${x^2} - 5xy + 6{y^2} = 0$ are

The combined equation of two lines passing through the origin and making an angle of $45^{\circ}$ with the line $3x + y = 0$ is:

The locus of a point which moves such that its distance from the origin is thrice its distance from the line $y = 2x$ 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

If one of the lines given by the equation $x^{2}+kxy+2y^{2}=0$ is $x+2y=0$,then $k=$

If the equation $2x^2 + 7xy + 3y^2 - 9x - 7y + k = 0$ represents a pair of lines,then $k$ is equal to