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

$A$ homogeneous equation of second degree in $x$ and $y$ represents which of the following?

If $x^2+\alpha y^2+2 \beta y=a^2$ represents a pair of perpendicular lines,then $\beta$ equals to

Assertion $(A)$: The difference of the slopes of the lines represented by $y^2 - 2xy \sec^2 \alpha + (3 + \tan^2 \alpha)(\tan^2 \alpha - 1) x^2 = 0$ is $4$.
Reason $(R)$: The difference of the slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ is $\frac{2 \sqrt{h^2 - ab}}{|b|}$.

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

If the ratio of gradients of the lines represented by $ax^2 + 2hxy + by^2 = 0$ is $1 : 3$,then the value of the ratio $h^2 : ab$ is