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

The combined equation of the two lines $ax+by+c=0$ and $a'x+b'y+c'=0$ can be written as $(ax+by+c)(a'x+b'y+c')=0$. The equation of the angle bisectors of the lines represented by the equation $2x^2+xy-3y^2=0$ is:

If the lines $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+ky-8=0$ are concurrent,then $k$ equals

If the pair of lines $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ intersect on the $y$-axis,then:

The equation of the pair of bisectors of the angles between the pair of straight lines $3x^2+7xy+2y^2+5x+5y+2=0$ is

If the bisectors of the angles between the pairs of lines given by the equations $ax^2 + 2hxy + by^2 = 0$ and $ax^2 + 2hxy + by^2 + \lambda(x^2 + y^2) = 0$ are coincident,then $\lambda = $