If $s$ and $p$ are respectively the sum and the product of the slopes of the lines $3x^2 - 2xy - 15y^2 = 0$,then $s:p$ is equal to

The joint equation of a pair of lines passing through the origin and making an angle of $\frac{\pi}{4}$ with the line $3x + 2y - 8 = 0$ is

If the sum and product of the slopes of the lines represented by $4x^2 + 2hxy - 7y^2 = 0$ are equal,then $h = \dots$

The separate equations of the lines represented by the equation $3x^{2}-2\sqrt{3}xy-3y^{2}=0$ are

If $m_{1}$ and $m_{2}$ are slopes of the lines represented by $(\sec^{2} \theta - \sin^{2} \theta) x^{2} - 2 \tan \theta xy + \sin^{2} \theta y^{2} = 0$,then $|m_{1} - m_{2}| = $

The equation of the image of the pair of lines $y = |x - 1|$ in the $y$-axis is: