The joint equation of the pair of lines passing through the point of intersection of the lines represented by $2x^{2}-xy-15y^{2}-7x+32y-9=0$ and parallel to the coordinate axes is:

If the lines $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+\lambda y-8=0$ are concurrent,then the value of $\lambda$ is

The equation of a pair of lines $y=px$ and $y=qx$ can be written as $(y-px)(y-qx)=0$. Then the equation of the pair of angle bisectors of the lines $x^2-4xy-5y^2=0$ is

If the pairs of straight lines $x^2-2 q x y-y^2=0$ and $x^2-2 p x y-y^2=0$ bisect the angles between each other,then which of the following is correct?

The equation of the bisectors of the angle between the lines represented by the equation ${x^2} - {y^2} = 0$ 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