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

The equation of the line passing through the points $(1, 2)$ and $(2, 5)$ is:

In what ratio is the line segment joining the points $(-1, 1)$ and $(5, 7)$ divided by the line $x + y = 4$?

The point $P(a, b)$ lies on the straight line $3x + 2y = 13$ and the point $Q(b, a)$ lies on the straight line $4x - y = 5$. Then the equation of the line $PQ$ is

What are the coordinates of a point on the line $2x + 3y + 7 = 0$ which is at a distance of $3$ units from the point $(1, -3)$?

Find the equation of the line whose perpendicular distance from the origin is $4$ units and the angle which the normal makes with the positive direction of the $x$-axis is $15^{\circ}$.