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

The equation $x^2 + ky^2 + 4xy = 0$ represents two coincident lines,if $k =$

$A$ pair of straight lines drawn through the origin forms an isosceles triangle right-angled at the origin with the line $2x + 3y = 6$. The area (in sq. units) of the triangle so formed is

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

If the angles made by the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ with the $X$-axis are $\alpha$ and $\beta$, then $\tan(\alpha + \beta)$ is

If one of the lines given by $k x^2 + x y - y^2 = 0$ bisects the angle between the coordinate axes,then the values of $k$ are