If the straight line $ax + by + c = 0$ always passes through $(1, -2),$ then $a, b, c$ are

Find the equation of the line passing through the point $(-1, 2)$ and parallel to the line $3x - 4y + 5 = 0$.

The lines $2x + 3y = 6$ and $2x + 3y = 8$ cut the $X$-axis at $A$ and $B$,respectively. $A$ line $L$ drawn through the point $(2, 2)$ meets the $X$-axis at $C$ in such a way that the abscissae of $A, B,$ and $C$ are in arithmetic progression. Then,the equation of the line $L$ is

The line $L_1$ passes through the points $(-1, 2)$ and $(3, 6)$. If $L_1$ divides the line $L_2$ (which passes through $(3, -1)$) in the ratio $1:3$ internally, and the point of intersection lies on $L_1$, find the equation of $L_2$ given that it is perpendicular to $L_1$.

The equation of the line passing through $(a, b)$ and parallel to the line $\frac{x}{a} + \frac{y}{b} = 1$ is

The polar equation $\cos \theta + 7 \sin \theta = \frac{1}{r}$ represents a