If the slopes of the lines represented by $ax^{2} + 2hxy + by^{2} = 0$ are in the ratio $1 : 3$,then $h^{2} : ab =$

The combined equation of a possible pair of adjacent sides of a square with area $16 \text{ square units}$ whose centre is the point of intersection of the lines $x+2y-3=0$ and $2x-y-1=0$ is

The joint equation of the pair of lines passing through $(3, -2)$ and parallel to the lines represented by $x^{2} - 4xy + 3y^{2} = 0$ is:

If one of the lines in the pair of straight lines given by $4x^2+6xy+ky^2=0$ bisects the angle between the coordinate axes,then $k \in$

If the equation $x^2 + y^2 + 2gx + 2fy + 1 = 0$ represents a pair of lines,then

The quadrilateral formed by the pairs of lines $xy+x+y+1=0$ and $xy+3x+3y+9=0$ is