If the equation $\lambda x^{2} + 2y^{2} - 5xy + 5x - 7y + 3 = 0$ represents a pair of straight lines,then $\lambda = \dots$

If the slope of one of the lines represented by $ax^2+2hxy+by^2=0$ is the square of the other,then $\frac{a+b}{h}+\frac{8h^2}{ab}$ is equal to:

The product of the perpendicular distances from the point $(2, -1)$ to the pair of lines represented by $2x^2 - 5xy + 2y^2 = 0$ is:

The equation $2y^2 - xy - x^2 + 6x - 8 = 0$ represents

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

The joint equation of the pair of lines passing through the origin and forming an equilateral triangle with the line $x=3$ is