The equation of the line passing through the point of intersection of the lines $3x - 2y - 1 = 0$ and $x - 4y + 3 = 0$ and the point $(\pi, 0)$ is:

For all values of $\theta$,the line $(2 \cos \theta + 3 \sin \theta) x + (3 \cos \theta - 5 \sin \theta) y - (5 \cos \theta - 2 \sin \theta) = 0$ passes through which fixed point?

$L_1$ and $L_2$ are two lines having slopes $2$ and $-\frac{1}{2}$ respectively. If both $L_1$ and $L_2$ are concurrent with the lines $x-y+2=0$ and $2x+y+3=0$,then the sum of the absolute values of the intercepts made by the lines $L_1$ and $L_2$ on the coordinate axes is:

Number of values of $m$ for which the lines $x + y - 1 = 0$,$(m - 1)x + (m^2 - 7)y - 5 = 0$ and $(m - 2)x + (2m - 5)y = 0$ are concurrent,are

If three lines whose equations are $y=m_{1}x+c_{1}$,$y=m_{2}x+c_{2}$,and $y=m_{3}x+c_{3}$ are concurrent,then show that $m_{1}(c_{2}-c_{3})+m_{2}(c_{3}-c_{1})+m_{3}(c_{1}-c_{2})=0$.

The lines $(a+2b)x + (a-3b)y = a-b$ for different values of $a$ and $b$ pass through a fixed point whose coordinates are: