The joint equation of the bisectors of the angles between the lines represented by $2x^2 + 11xy + 3y^2 = 0$ is:

The joint equation of the bisectors of the angle between the lines represented by $3x^{2} + 2xy - y^{2} = 0$ is:

The ratio in which the line $x+y-1=0$ divides the line segment joining the origin $(0,0)$ and the point of intersection of the lines represented by $2x^2-13xy-7y^2+x+23y-6=0$ is

If the line $y=mx$ is one of the bisectors of $x^2+4xy-y^2=0$,then the value of $2m$ is:

If the lines represented by $x^2-2hxy-y^2=0$ are rotated about $(0,0)$ through an angle $\alpha$,one in the clockwise direction and the other in the counter-clockwise direction,then the combined equation of the bisectors of the angle between the lines thus obtained is

If the equation $16x^2 - 24xy + 9y^2 - 8x + 6y - 35 = 0$ represents a pair of straight lines, then the equation of the locus of points equidistant from these two lines is...