If the slope of one line is twice the slope of the other in the pair of straight lines $ax^2+2hxy+by^2=0$,then $8h^2$ is equal to (in $ab$)

The value of $\lambda$ with $|\lambda| < 16$ such that $2 x^2-10 x y+12 y^2+5 x+\lambda y-3=0$ represents a pair of straight lines,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 $k \in$

The combined equation of a pair of lines passing through the origin and inclined at $60^{\circ}$ and $30^{\circ}$ respectively with the $x$-axis 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:

The joint equation of two lines passing through $(-2, 3)$ and parallel to the bisectors of the angle between the co-ordinate axes is