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

If the line $y = mx$ bisects the angle between the lines $ax^2 + 2hxy + by^2 = 0$,then $m$ is a root of the quadratic equation:

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 $pq=$

The area of the triangle formed by the line $x + y = 3$ and the angle bisectors of the pair of lines $x^2 - y^2 + 2y = 1$ is:

The combined equation of lines parallel to the coordinate axes and passing through the point of intersection of lines represented by $x^2 - 6xy + 5y^2 + 10x - 14y + 9 = 0$ 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