The equation $xy + a^2 = a(x + y)$ represents

The combined equation of a possible pair of adjacent sides of a square with area $16 \text{ square units}$ whose centre is the point of intersection of the lines $x+2y-3=0$ and $2x-y-1=0$ is

If the equation $ax^{2} + by^{2} + cx + cy = 0$,$c \neq 0$ represents a pair of lines,then

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

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

If one of the lines given by the pair of lines $3x^2 + axy - 2y^2 = 0$ makes an angle of $60^{\circ}$ with the $x$-axis,then $a=$