If one of the lines represented by $ax^2 + 2hxy + by^2 = 0$ bisects the angle between the positive coordinate axes,then

The joint equation of the pair of lines passing through the origin with slopes $(1+\sqrt{2})$ and $\frac{1}{(1+\sqrt{2})}$ is

The combined equation of the straight lines of the form $y=kx+1$ (where $k$ is an integer) such that the point of intersection of each with the line $3x+4y=9$ has an integer as its $x$-coordinate is

The joint equation of the pair of lines passing through the origin and forming an equilateral triangle with the line $y=5$ is

The equation of a pair of lines is given by a second-degree homogeneous equation. If one of them is perpendicular to the line $x+2y+7=0$ and the other is parallel to the line $3x+4y+5=0$,then the equation of that pair of lines is:

Find the equation of the pair of lines passing through the origin and perpendicular to the pair of lines given by $5x^2 - 7xy - 3y^2 = 0$.