If one of the lines given by the equation $x^{2}+kxy+2y^{2}=0$ is $x+2y=0$,then $k=$

If $p_1$ and $p_2$ denote the lengths of perpendiculars from $(2,3)$ onto the lines given by $15 x^2+31 x y+14 y^2=0$,and if $p_1 > p_2$,then $p_1^2 + \frac{1}{74} - p_2^2 + \frac{1}{13}$ is equal to

If the distance of two lines passing through the origin from the point $({x_1}, {y_1})$ is $d$,then the equation of the lines is:

The combined equation of two lines $L$ and $L_1$ is $2x^2+axy+3y^2=0$ and the combined equation of two lines $L$ and $L_2$ is $2x^2+bxy-3y^2=0$. If $L_1$ and $L_2$ are perpendicular,then $a^2+b^2=$

If the slope of one line of the pair of lines $2x^2 + hxy + 6y^2 = 0$ is thrice the slope of the other line,then $h =$

If the slopes of the lines given by the equation $ax^{2} + 2hxy + by^{2} = 0$ are in the ratio $5:3$,then the ratio $h^{2}:ab$ is: