If the lines $L_1 \equiv x-2y+3=0$,$L_2 \equiv 2x+y+1=0$,and $L_3 \equiv 3x+y+c=0$ are concurrent and $\theta$ is the acute angle between the lines $L_1=0$ and $L_3=0$,then $\tan \theta=$

For the family of lines given by the equation $(2 + k)x + (1 + k)y = 5 + 7k$,which of the following statements is true for different values of $k$?

What is the nature of the points $(-a, -b)$,$(0, 0)$,$(a, b)$,and $(a^2, ab)$?

If $\pi / 3$ is the angle between the straight lines $px + qy + r = 0$ and $x \sin \alpha + y \cos \alpha = r$ $(r \neq 0)$ which meet at a point $A$,and the straight line $x \cos \alpha - y \sin \alpha = 0$ also passes through the point $A$,then:

If the lines $4x + 3y - k = 0$,$2x + y + 3 = 0$,and $3x + 2y + k = 0$ are concurrent,then the perpendicular distance from the point of concurrency of these lines to the line $3x + 4y + 2 = 0$ is

Find the equation of the line passing through the intersection of the lines $x + y - 3 = 0$ and $2x - y + 1 = 0$ and the point $(2, -3)$.