For what value of $k$ does the equation $kx^2 - 10xy + 12y^2 + 5x - 16y - 3 = 0$ represent a pair of straight lines?

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 the pair of lines passing through the origin and forming an equilateral triangle with the line $y=3$ is

The equation $\frac{x^2}{a} + \frac{xy}{h} + \frac{y^2}{b} = 0$ $(a \neq 0, h \neq 0, b \neq 0)$ represents two coincident lines if:

The equation $x^2 - 2\sqrt{3}xy + 2y^2 = 0$ represents two sides of a triangle. If the angle between them is $\frac{\pi}{3}$,then the perimeter of that triangle is

The equation of the line common to the pair of lines $(p^2-q^2) x^2+(q^2-r^2) xy+(r^2-p^2) y^2=0$ and $(l-m) x^2+(m-n) xy+(n-l) y^2=0$ is