The equation $2x^2 + 4xy - ky^2 + 4x + 2y - 1 = 0$ represents a pair of lines. The value of $k$ is

The equation $2x^2 + 7xy + 3y^2 + 8x + 14y + \lambda = 0$ represents a pair of straight lines when $\lambda = $

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

If $P_1$ and $P_2$ are perpendicular distances (in units) from point $(2, -1)$ to the pair of lines $2x^2 - 5xy + 2y^2 = 0$,then the value of $P_1 P_2$ is

If the equation $\lambda x^2 + 2y^2 - 5xy + 5x - 7y + 3 = 0$ represents two straight lines,then the value of $\lambda$ is:

If the slope of one of the two lines represented by the equation $\frac{x^2}{a} + \frac{2xy}{h} + \frac{y^2}{b} = 0$ is twice that of the other, then find the ratio $h^2 : ab$.