The equation $x^2 + kxy + y^2 - 5x - 7y + 6 = 0$ represents a pair of straight lines,then $k$ is

If the lines represented by the equation $ax^2 - bxy - y^2 = 0$ make angles $\alpha$ and $\beta$ with the $x$-axis,then $\tan(\alpha + \beta) = $

If the lines represented by the equation $4xy + 6x - 8y + c = 0$ form a rectangle with the coordinate axes,then the area of the rectangle (in sq. units) is

If $2x^2 + 3xy - 2y^2 - 5x + fy - 3 = 0$ represents a pair of straight lines,then one of the possible values of $f$ is

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 joint equation of a pair of straight lines passing through the origin and having slopes $(1+\sqrt{2})$ and $\left(\frac{1}{1+\sqrt{2}}\right)$ is $......$