If the equation given by $hxy + 10x + 6y + 4 = 0$ represents a pair of lines,then $h$ is equal to

The value of $\lambda$ such that $\lambda x^2-10 x y+12 y^2+5 x-16 y-3=0$ represents a pair of straight lines is:

If the equation $kxy + 10x + 8y + 16 = 0$ represents a pair of lines,then

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 $\frac{2 \sqrt{h^2 - ab}}{|b|}$.

The joint equation of the pair of lines passing through the origin and forming an equilateral triangle with the line $y=4$ is

The combined equation of the straight lines of the form $y=kx+1$ (where $k$ is an integer) such that the point of intersection of each with the line $3x+4y=9$ has an integer as its $x$-coordinate is