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

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

The condition for the general quadratic equation $f(x, y) = ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ to represent coincident lines is:

The joint equation of the bisectors of the angles between the lines $x=5$ and $y=3$ is

If the pair of lines $x^2-16pxy-y^2=0$ and $x^2-16qxy-y^2=0$ are such that each pair bisects the angle between the other pair,then $pq=$